Predicting the long-term durability of limestones subjected to freeze–thaw cycles (case study: Guilan province, north of Iran)

Document Type : Research Paper

Authors

Department of Geology,Faculty of Science , Bu-Ali Sina University, Hamedan,Iran

Abstract

Mesozoic limestones with Cretaceous and Jurassic age are widely seen in the Guilan province, north of
Iran. Regarding the climate of this area, the development of limestone with a high percent of CaCO3
(rather than 80%) and karst morphology development was investigated to evaluate the effect of freezingthawing (F-T) cycles concerning the karst development. In this way, the physical and mechanical
properties of the four lithology units (Kl1, Kl2, Km2, and Jkl) were assessed before and after F-T cycles
to study the weathering effects. The survey of the petrography of rocks shows that the samples were
grainstone and packstone type, according to Donham classification. The highest deterioration occurred
in sample Kl2 after 60 F-T cycles. The physical and mechanical properties of rock samples such as ɣ
(unit weight), wa (water absorption), Pv (P-wave velocity), and UCS (uniaxial compressive strength) for
both dry and saturated conditions, and after 60 cycles of freezing-thawing (F-T) were attained. The
softening coefficient (K1) and freezing coefficient (K2) of samples were calculated using the UCS
values. The F-T cycles caused significant losses in the UCS values. The measured Vp during the F-T
cycles provided a suitable tool for calculating the damage value and decayed constant (λ). This study
showed that the F-T test is capable of creating microcrack and fractures within the rock as the initial
factors for increasing the contact surface in the dissolution process. The increase in Dn (damage
variable), porosity, water absorption, and decrease of Vp after 60 F-T cycles confirm this result. Also,
the increase in tangent Young’s modulus and decrease in strain show that the samples were brittle after
60 F-T periods. Therefore, it is concluded that the freezing and softening coefficient and Vp are effective
tools for assessing the rock damage during F-T periods. 

Keywords

Main Subjects


Article Title [فارسی]

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Abdelhamid, M.M.A., Li, D., Ren, G., 2020. Predicting Unconfined Compressive Strength Decrease of
Carbonate Building Materials against Frost Attack Using Nondestructive Physical Tests.
Sustainability, 12:1379, 1-18.##
Andriani, G.F., Walsh, N., 2007. Rocky coast geomorphology and erosional processes: a case study
along the Murgia coastline South of Bari, Apulia—SE Italy. Geomorphology, 87: 224-238.##
Andriani, G.F., Germinario, L., 2014. Thermal decay of carbonate dimension stones: fabric, physical
394 Dehban Avan Stakhri et al.
and mechanical changes. Environmental Earth Science, 72: 2523-2539.##
Attewell, P.B., Farmer, I.W., 1976. Principles of engineering geology, Chapman and Hall,
London.1075pp.##
Anon, O.H., 1979. Classification of rocks and soils for engineering geological mapping. Part 1: rock
and soil materials. Bulletin of Engineering Geology and the Environment, 19: 355-371.##
ASTM., 1995. Standard test method for unconfined compressive strength of intact rock core specimens.
ASTM standards on disc 04.08, Designation, D2938.##
ASTM., 1996. Standard test method for laboratory determination of pulse velocities and ultrasonic
elastic constants of rock. Designation, D2845-D2895.##
ASTM., 2001b. Standard method for determination of the point load strength index of rock. ASTM
standards on disc 04.08, Designation, D5731.##
ASTM., 2004. Standard Test Method for Evaluation of Durability of Rock for Erosion Control Under
Freezing and Thawing Conditions. Designation, D5312 - 04.##
ASTM., 2011. Standard Test Method for Base Number Determination by Potentiometric
Hydrochloric Acid Titration, ASTM international, West Conshohocken, PA, 2003,
Standard D4739.##
Al-Omari, A., Beck, K., Brunetaud, X., Török, Á., Al-Mukhtar, M., 2015. Critical degree of saturation:
A control factor of freeze-thaw damage of porous limestones at Castle of Chambord, France.
Engineering Geology, 185: 71-80.##
Bayram, F., 2012. Predicting mechanical strength loss of natural stones after freeze-thaw in cold regions.
Cold Regions Science and Technology, 84: 98-102.##
Bednarik, M., Moshammer, B., Heinrich, M., Holzer, R., Laho, M., Rabeder, J., Uhlir, C.H.,
Unterwurzacher, M., 2014. Engineering geological properties of Leitha Limestone from historical
quarries in Burgenland and Styria, Austria. Engineering Geology, 176: 66-78.##
Beier, N.A., Sego, D.C., 2009. Cyclic freeze-thaw to enhance the stability of coal tailings. Cold Regions
Science and Technology, 55: 278-285.##
Bellanger, M., Homand, F., Remy, J.M., 1993. Water behaviour in limestones as a function of pores
structure: application to frost resistance of some Lorraine limestones, Engineering Geology, 36: 99-
108.##
Bieniawski, Z.T., 1975. The point load test in geotechnical practice, Engineering Geology, 9: 1-11.##
Bortz , S.A., Wonneberger, B., 1997. Laboratory evaluation of building stone weathering. In: Labuz,
J.S., (Ed.), Degradation of Natural Building Stone. Geotechnical Special Publications, 72: 85-104.##
Broch, E., Franklin, J.A., 1972. The point-load strength test. International Journal Rock Mechanic and
Mining Sciences & Geomechanics Abstract, 9: 669-698.##
Chen, C.H., Yeung, M.R., Mori, N., 2004. Effect of water saturation on deterioration of welded tuff due
to freeze-thaw action. Cold Regions Sciences Technolology, 38: 127-136.##
De Kock, T., Turmel, A., Fronteau, G., Cnudde, V., 2017. Rock fabric heterogeneity and its influence
on the petrophysical properties of a building limestone: Lede stone (Belgium) as an example.
Engineering Geology, 216: 31-41.##
Domenico, S.N., 1984. Rock lithology and porosity determination from shear and compressional wave
velocity. Geophysics, 49: 1188-1195.##
Eslami, J., Walbert, C.H., Beaucour, A., Bourges, A., Noumowe, A., 2018. Influence of physical and
mechanical properties on the durability of limestone subjected to freeze-thaw cycles. Construction
and Building Materials, 162: 420-429.##
Everett, D.H., 1961. The thermodynamics of frost damage to porous solids, Transactions of the Faraday
Society, 57: 1541-1551.##
Fereidooni, D., Khajevand, R., 2017. Correlations Between Slake-Durability Index and Engineering
Properties of Some Travertine Samples Under Wetting Drying Cycles. Journal of Geotechnical
Engineering, 36: 1071-1089.##
Fookes, P.G., Dearman, W.R., Franklin, J.A., 1971, Some engineering aspects of rock weathering with
field examples from Dartmoor and elsewhere. Quarterly Journal of Engineering Geology and
Hydrogeology, 5: 139-185.##
Ghobadi, M.H., Torabi-Kaveh, M., 2014. Assessing the potential for deterioration of limestones forming
Taq-e Bostan monuments under freeze-thaw weathering and karst development. Environmental
Earth Sciences, 72: 5035-5047.Abdelhamid, M.M.A., Li, D., Ren, G., 2020. Predicting Unconfined Compressive Strength Decrease of
Carbonate Building Materials against Frost Attack Using Nondestructive Physical Tests.
Sustainability, 12:1379, 1-18.##
Andriani, G.F., Walsh, N., 2007. Rocky coast geomorphology and erosional processes: a case study
along the Murgia coastline South of Bari, Apulia—SE Italy. Geomorphology, 87: 224-238.##
Andriani, G.F., Germinario, L., 2014. Thermal decay of carbonate dimension stones: fabric, physical
394 Dehban Avan Stakhri et al.
and mechanical changes. Environmental Earth Science, 72: 2523-2539.##
Attewell, P.B., Farmer, I.W., 1976. Principles of engineering geology, Chapman and Hall,
London.1075pp.##
Anon, O.H., 1979. Classification of rocks and soils for engineering geological mapping. Part 1: rock
and soil materials. Bulletin of Engineering Geology and the Environment, 19: 355-371.##
ASTM., 1995. Standard test method for unconfined compressive strength of intact rock core specimens.
ASTM standards on disc 04.08, Designation, D2938.##
ASTM., 1996. Standard test method for laboratory determination of pulse velocities and ultrasonic
elastic constants of rock. Designation, D2845-D2895.##
ASTM., 2001b. Standard method for determination of the point load strength index of rock. ASTM
standards on disc 04.08, Designation, D5731.##
ASTM., 2004. Standard Test Method for Evaluation of Durability of Rock for Erosion Control Under
Freezing and Thawing Conditions. Designation, D5312 - 04.##
ASTM., 2011. Standard Test Method for Base Number Determination by Potentiometric
Hydrochloric Acid Titration, ASTM international, West Conshohocken, PA, 2003,
Standard D4739.##
Al-Omari, A., Beck, K., Brunetaud, X., Török, Á., Al-Mukhtar, M., 2015. Critical degree of saturation:
A control factor of freeze-thaw damage of porous limestones at Castle of Chambord, France.
Engineering Geology, 185: 71-80.##
Bayram, F., 2012. Predicting mechanical strength loss of natural stones after freeze-thaw in cold regions.
Cold Regions Science and Technology, 84: 98-102.##
Bednarik, M., Moshammer, B., Heinrich, M., Holzer, R., Laho, M., Rabeder, J., Uhlir, C.H.,
Unterwurzacher, M., 2014. Engineering geological properties of Leitha Limestone from historical
quarries in Burgenland and Styria, Austria. Engineering Geology, 176: 66-78.##
Beier, N.A., Sego, D.C., 2009. Cyclic freeze-thaw to enhance the stability of coal tailings. Cold Regions
Science and Technology, 55: 278-285.##
Bellanger, M., Homand, F., Remy, J.M., 1993. Water behaviour in limestones as a function of pores
structure: application to frost resistance of some Lorraine limestones, Engineering Geology, 36: 99-
108.##
Bieniawski, Z.T., 1975. The point load test in geotechnical practice, Engineering Geology, 9: 1-11.##
Bortz , S.A., Wonneberger, B., 1997. Laboratory evaluation of building stone weathering. In: Labuz,
J.S., (Ed.), Degradation of Natural Building Stone. Geotechnical Special Publications, 72: 85-104.##
Broch, E., Franklin, J.A., 1972. The point-load strength test. International Journal Rock Mechanic and
Mining Sciences & Geomechanics Abstract, 9: 669-698.##
Chen, C.H., Yeung, M.R., Mori, N., 2004. Effect of water saturation on deterioration of welded tuff due
to freeze-thaw action. Cold Regions Sciences Technolology, 38: 127-136.##
De Kock, T., Turmel, A., Fronteau, G., Cnudde, V., 2017. Rock fabric heterogeneity and its influence
on the petrophysical properties of a building limestone: Lede stone (Belgium) as an example.
Engineering Geology, 216: 31-41.##
Domenico, S.N., 1984. Rock lithology and porosity determination from shear and compressional wave
velocity. Geophysics, 49: 1188-1195.##
Eslami, J., Walbert, C.H., Beaucour, A., Bourges, A., Noumowe, A., 2018. Influence of physical and
mechanical properties on the durability of limestone subjected to freeze-thaw cycles. Construction
and Building Materials, 162: 420-429.##
Everett, D.H., 1961. The thermodynamics of frost damage to porous solids, Transactions of the Faraday
Society, 57: 1541-1551.##
Fereidooni, D., Khajevand, R., 2017. Correlations Between Slake-Durability Index and Engineering
Properties of Some Travertine Samples Under Wetting Drying Cycles. Journal of Geotechnical
Engineering, 36: 1071-1089.##
Fookes, P.G., Dearman, W.R., Franklin, J.A., 1971, Some engineering aspects of rock weathering with
field examples from Dartmoor and elsewhere. Quarterly Journal of Engineering Geology and
Hydrogeology, 5: 139-185.##
Ghobadi, M.H., Torabi-Kaveh, M., 2014. Assessing the potential for deterioration of limestones forming
Taq-e Bostan monuments under freeze-thaw weathering and karst development. Environmental
Earth Sciences, 72: 5035-5047.##
González, J., Saldaña, M., Arzúa, J., 2019. Analytical Model for Predicting the UCS from P-Wave
Velocity, Density, and Porosity on Saturated Limestone. Applied Sciences, 9(23): 52-65.##
Han, D.H., Nur, A., Morgan, D., 1986. Effects of porosity and clay content on wave velocities in
sandstones. Geophysics, 51: 2093-2107.##
Hashemi, M., Bashiri Goudarzi, M., Jamshidi, A., 2018. Experimental investigation on the performance
of Schmidt hammer test in durability assessment of carbonate building stones against freeze-thaw
weathering. Environmental Earth Sciences, 77(684):1-15.##
Hassanvand, M., Moradi, S., Fattahi, M., Zargar, G.H., 2018. Estimation of rock uniaxial compressive
strength for an Iranian carbonate oil reservoir: Modeling vs. artificial neural network application.
Petroleum Research, 3: 336-345.##
Hori, M., Morihiro, H., 1998. Micromechanical analysis on deterioration due to freezing and thawing
in porous brittle materials. International Journal of Engineering Science, 36: 511-522.##
ISRM., 1981. ISRM suggested methods. In: Brown, E.T., (Ed.), Rock characterization, testing and
monitoring. Pergamon Press, London, 211pp.##
Jamshidi, A., Zamanian, H., Zarei Sahamieh, R., 2018. The effect of density and porosity on the
correlation between uniaxial compressive strength and P-wave velocity. Rock mechanics and Rock
engineering, 51(4): 1279-1286.##
Jamshidi, A., Nikudel, M.R., Khamehchiyan, M., 2016. Evaluation of the durability of Gerdoee
travertine after freeze-thaw cycles in fresh water and sodium sulfate solution. Engineering Geology,
202: 36-43.##
Jamshidi, A., Nikudel, M.R., Khamehchiyan, M., 2015. Estimating the engineering properties of
building stones after freeze-thaw using multiple regression analysis. Iranian Journal of Sciences and
Technology, Transaction A: Science, 39A2: 147-163.##
Jamshidi, A., Nikudel, M.R., Khamehchiyan, M., 2013. Predicting the long-term durability of building
stones against freeze-thaw using a decay function model. Cold Regions Sciences and Technology,
92: 29-36.##
Khanlari, G.R, Heidari, M, Sepahi-Gero, A. A, Fereidooni, D., 2014. Quantification of strength
anisotropy of metamorphic rocks of the Hamedan province, Iran, as determined from cylindrical
punch, point load and Brazilian tests. Engineering Geology, 169: 80-90.##
Koch, A., Siegesmund, S., 2004. The combined effect of moisture and temperature on the anomalous
expansion behaviour of marble. Environmental Geology, 46: 350-363.##
Luque, A., Ruiz-Agudo, E., Cultrone, G., Sebastia´n, E., Siegesmund, S., 2011. Direct observation of
microcrack development in marble caused by thermal weathering. Environmental Earth Sciences,
62: 1375-1386.##
Multuturk, M., Altindag, R., Turk, G., 2004. A decay function model for the integrity loss of rock when
subjected to recurrent cycles of freezing-thawing and heating-cooling, International Journal of Rock
Mechanics and Mining Sciences, 41: 237-244.##
Matsuoka, N., 1990. Mechanisms of rock breakdown by frost action: an experimental approach. Cold
Regions Sciences and Technology, 17: 253-270.##
Nicholson, H., Dawn, T., Nicholson, F.H., 2000. Physical deterioration of sedimentary rocks subjected
to experimental freeze-thaw weathering. Earth Surface Processes and Landforms, 25: 1295-1307.##
Oda, M., Suzuki, K., Maeshibu, T., 1984. Elastic compliance for rock-like materials with random cracks.
Soils and Foundations, 24: 27-40.##
Pápay, Z., 2018. Effect of Thermal and Freeze-thaw Stress on the Mechanical Properties of Porous
Limestone. Periodica Polytechnica Civil Engineering, 62(2): 423-428.##
Plevova´, E., Kozˇusˇnı´kova´, A., Vaculı´kova´, L., Simha Martynkova´, G., 2010. Thermal behavior
of selected Czech marble samples. Journal of Thermal Analysis and Calorimetry, 101: 657-664.##
Proskin, S., Sego, D., Alostaz, M., 2010. Freeze-thaw and consolidation tests on Suncor mature fine
tailings (MFT). Cold Regions Sciences and Technology, 63: 110-120.##
Powers, T.C., Helmuth, R. A., 1953. Theory of volume changes in hardened Portland cement paste
during freezing. Proceedings of the annual meeting - Highway Research Boar, 32: 285- 297.##
Ruedrich, J., Kirchner, D., Siegesmund, S., 2011. Physical weathering of building stones induced by
freeze-thaw action: a laboratory longterm study. Environmental Earth Sciences, 63: 1573-1586.##
Royer-Carfagni, G. F., 1999. On the thermal degradation of marble. International Journal of Rock
396 Dehban Avan Stakhri et al.
Mechanics and Mining Sciences, 36: 119-126.##
Saad, A., Guedon, S., Martineau, F., 2010. Microstructural weathering of sedimentary rocks by freezethaw
cycles: experimental study of state and transfer parameters. Comptes Rendus Geoscience, 342:
197-203.##
Setzer, M.J., Seter, M., Auberg, R., 1997. Basis of testing the freeze-thaw resistance Surface and internal
deterioration. E & FN Spon London, pp. 157-173.##
Shalabi, F. I., Cording, E. J., Al-Hattamleh, O. H., 2007. Estimation of rock engineering properties using
hardness tests. Engineering Geology, 90: 138-147.##
Siegesmund, S., Ullemeyer, K., Weiss, T., Tschegg, E.K., 2000. Physical weathering of marbles caused
by anisotropic thermal expansion. International Journal of Earth Sciences, 89: 170-182.##
Siegesmund, S., Weiss, T., Vollbrecht, A., 2002. Natural Stone, Weathering Phenomena, Conservation
Strategies and Case Studies. Geological Society, London, 205pp.##
Siegesmund, S., Grimm, W.D., Du¨rrast, H., Ruedrich, J., 2010. Limestones in Germany used as
building stones: an overview. In: Smith, B. J., Go´mez-Heras, M., Viles, H. A., Cassar, J., (Ed.),
Limestone in the built environment: present-day challenges for the preservation of the past.
Geological Society, London, pp 37-59.##
Siegesmund, S., Dürrast, H., 2014. Physical and mechanical properties of rocks. In: Siegesmund, S.,
Snethlage, R., (Ed.), Stone in architecture, 5th edn. Springer, Berlin, pp 97-225.##
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pp 65-80.##
González, J., Saldaña, M., Arzúa, J., 2019. Analytical Model for Predicting the UCS from P-Wave
Velocity, Density, and Porosity on Saturated Limestone. Applied Sciences, 9(23): 52-65.##
Han, D.H., Nur, A., Morgan, D., 1986. Effects of porosity and clay content on wave velocities in
sandstones. Geophysics, 51: 2093-2107.##
Hashemi, M., Bashiri Goudarzi, M., Jamshidi, A., 2018. Experimental investigation on the performance
of Schmidt hammer test in durability assessment of carbonate building stones against freeze-thaw
weathering. Environmental Earth Sciences, 77(684):1-15.##
Hassanvand, M., Moradi, S., Fattahi, M., Zargar, G.H., 2018. Estimation of rock uniaxial compressive
strength for an Iranian carbonate oil reservoir: Modeling vs. artificial neural network application.
Petroleum Research, 3: 336-345.##
Hori, M., Morihiro, H., 1998. Micromechanical analysis on deterioration due to freezing and thawing
in porous brittle materials. International Journal of Engineering Science, 36: 511-522.##
ISRM., 1981. ISRM suggested methods. In: Brown, E.T., (Ed.), Rock characterization, testing and
monitoring. Pergamon Press, London, 211pp.##
Jamshidi, A., Zamanian, H., Zarei Sahamieh, R., 2018. The effect of density and porosity on the
correlation between uniaxial compressive strength and P-wave velocity. Rock mechanics and Rock
engineering, 51(4): 1279-1286.##
Jamshidi, A., Nikudel, M.R., Khamehchiyan, M., 2016. Evaluation of the durability of Gerdoee
travertine after freeze-thaw cycles in fresh water and sodium sulfate solution. Engineering Geology,
202: 36-43.##
Jamshidi, A., Nikudel, M.R., Khamehchiyan, M., 2015. Estimating the engineering properties of
building stones after freeze-thaw using multiple regression analysis. Iranian Journal of Sciences and
Technology, Transaction A: Science, 39A2: 147-163.##
Jamshidi, A., Nikudel, M.R., Khamehchiyan, M., 2013. Predicting the long-term durability of building
stones against freeze-thaw using a decay function model. Cold Regions Sciences and Technology,
92: 29-36.##
Khanlari, G.R, Heidari, M, Sepahi-Gero, A. A, Fereidooni, D., 2014. Quantification of strength
anisotropy of metamorphic rocks of the Hamedan province, Iran, as determined from cylindrical
punch, point load and Brazilian tests. Engineering Geology, 169: 80-90.##
Koch, A., Siegesmund, S., 2004. The combined effect of moisture and temperature on the anomalous
expansion behaviour of marble. Environmental Geology, 46: 350-363.##
Luque, A., Ruiz-Agudo, E., Cultrone, G., Sebastia´n, E., Siegesmund, S., 2011. Direct observation of
microcrack development in marble caused by thermal weathering. Environmental Earth Sciences,
62: 1375-1386.##
Multuturk, M., Altindag, R., Turk, G., 2004. A decay function model for the integrity loss of rock when
subjected to recurrent cycles of freezing-thawing and heating-cooling, International Journal of Rock
Mechanics and Mining Sciences, 41: 237-244.##
Matsuoka, N., 1990. Mechanisms of rock breakdown by frost action: an experimental approach. Cold
Regions Sciences and Technology, 17: 253-270.##
Nicholson, H., Dawn, T., Nicholson, F.H., 2000. Physical deterioration of sedimentary rocks subjected
to experimental freeze-thaw weathering. Earth Surface Processes and Landforms, 25: 1295-1307.##
Oda, M., Suzuki, K., Maeshibu, T., 1984. Elastic compliance for rock-like materials with random cracks.
Soils and Foundations, 24: 27-40.##
Pápay, Z., 2018. Effect of Thermal and Freeze-thaw Stress on the Mechanical Properties of Porous
Limestone. Periodica Polytechnica Civil Engineering, 62(2): 423-428.##
Plevova´, E., Kozˇusˇnı´kova´, A., Vaculı´kova´, L., Simha Martynkova´, G., 2010. Thermal behavior
of selected Czech marble samples. Journal of Thermal Analysis and Calorimetry, 101: 657-664.##
Proskin, S., Sego, D., Alostaz, M., 2010. Freeze-thaw and consolidation tests on Suncor mature fine
tailings (MFT). Cold Regions Sciences and Technology, 63: 110-120.##
Powers, T.C., Helmuth, R. A., 1953. Theory of volume changes in hardened Portland cement paste
during freezing. Proceedings of the annual meeting - Highway Research Boar, 32: 285- 297.##
Ruedrich, J., Kirchner, D., Siegesmund, S., 2011. Physical weathering of building stones induced by
freeze-thaw action: a laboratory longterm study. Environmental Earth Sciences, 63: 1573-1586.##
Royer-Carfagni, G. F., 1999. On the thermal degradation of marble. International Journal of Rock
396 Dehban Avan Stakhri et al.
Mechanics and Mining Sciences, 36: 119-126.##
Saad, A., Guedon, S., Martineau, F., 2010. Microstructural weathering of sedimentary rocks by freezethaw
cycles: experimental study of state and transfer parameters. Comptes Rendus Geoscience, 342:
197-203.##
Setzer, M.J., Seter, M., Auberg, R., 1997. Basis of testing the freeze-thaw resistance Surface and internal
deterioration. E & FN Spon London, pp. 157-173.##
Shalabi, F. I., Cording, E. J., Al-Hattamleh, O. H., 2007. Estimation of rock engineering properties using
hardness tests. Engineering Geology, 90: 138-147.##
Siegesmund, S., Ullemeyer, K., Weiss, T., Tschegg, E.K., 2000. Physical weathering of marbles caused
by anisotropic thermal expansion. International Journal of Earth Sciences, 89: 170-182.##
Siegesmund, S., Weiss, T., Vollbrecht, A., 2002. Natural Stone, Weathering Phenomena, Conservation
Strategies and Case Studies. Geological Society, London, 205pp.##
Siegesmund, S., Grimm, W.D., Du¨rrast, H., Ruedrich, J., 2010. Limestones in Germany used as
building stones: an overview. In: Smith, B. J., Go´mez-Heras, M., Viles, H. A., Cassar, J., (Ed.),
Limestone in the built environment: present-day challenges for the preservation of the past.
Geological Society, London, pp 37-59.##
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  • Receive Date: 25 January 2021
  • Revise Date: 27 March 2021
  • Accept Date: 18 April 2021
  • First Publish Date: 18 April 2021