ارزیابی تأثیر اندازه نمونه در سنگ های رسوبی و اندازه سنگدانه در نمونه بتنی بر مقاومت فشاری تک محوره

نوع مقاله: مقاله پژوهشی

نویسندگان

1 دانشکده مهندسی معدن، دانشگاه صنعتی اصفهان

2 دانشگاه کرتین استرالیا

10.29252/anm.8.16.57

چکیده

در مهندسی سنگ، انتخاب اندازه مناسب نمونه برای تعیین مقاومت فشاری سنگ که معرف خواص مقاومتی سنگ باشد، بسیار مهم است. پیش‌بینی مقاومت فشاری تک محوره در قطرهای مختلف با استفاده از تئوری‌های تأثیر اندازه نمونه بسیار با ارزش است. این تئوری‌ها، به پنج مدل تجربی، آماری، مولتی فراکتال، نظریه شکست و  نظریه شکست فراکتال تقسیم‌بندی شده‌اند. بررسی‌های محدودی برای تعیین همبستگی تئوری‌های تأثیر اندازه با نتایج آزمایش‌های تجربی در طبقه‌بندی‌های مختلف، بر روی سنگ‌ها و نمونه‌های مصنوعی انجام شده است. در این مقاله، مؤلفان با مروری بر مطالعات گذشته، تأثیر اندازه نمونه را روی مقاومت فشاری تک محوره سنگ‌های رسوبی و نمونه‌های مصنوعی با استفاده از مدل‌های تأثیر اندازه و تحلیل‌های آماری بررسی کرده‌اند. همچنین در مطالعه تجربی، 84 نمونه بتنی با چهار قطر 56، 68، 72 و 94 میلی‌متر و با سه دانه‌بندی مختلف 12-0، 20-0 و 25-0 میلی‌متر ساخته شد. یافته‌ها نشان داد که در سنگ‌های رسوبی، بررسی تأثیر اندازه نمونه با استفاده از نظریه شکست، همبستگی خوبی با نتایج آزمایش‌های تجربی دارد. در نمونه‌های مصنوعی، مدل هوک و براون مقادیر بالایی از ضرایب  را نشان داد، اما این مدل برای نمونه‌های با قطرهای بزرگ، محافظه کارانه است. در این قطرها، مدل مولتی فراکتال همبستگی بهتری با اطلاعات آزمایشگاهی دارد. نتایج مطالعات تجربی نشان داد که در دانه‌بندی‌های 20-0 و 25-0 میلی‌متر، با افزایش قطر، مقاومت فشاری تک محوره، ابتدا روند افزایشی و سپس روند کاهشی دارد. در نمونه‌های با دانه‌بندی 12-0 میلی‌متر، مقاومت فشاری یک روند افزایشی با افزایش قطر نشان داد. در نمونه‌های بتنی با دانه‌بندی ریز، مدل‌های مولتی فراکتال و تأثیر اندازه با استفاده از نظریه شکست، روند صعودی تغییرات مقاومت را به خوبی نشان می‌دهند. همچنین در نمونه‌های با دانه‌بندی درشت، مدل مولتی فراکتال، بیش‌ترین ضرائب  را نشان داد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Evaluation of Specimen Size-Effect in Sedimentary Rocks and Grain Size Effect in Concrete Specimens on Uniaxial Compressive Strength

نویسندگان [English]

  • Mohammad Darbor 1
  • Lohrasb Faramarzi 1
  • Mostafa Sharifzadeh 2
  • Hooman Rezaei 1
1 Dept. of Mining, Isfahan University of Technology
2 Curtin University, Australia
چکیده [English]

Summary
In rock engineering, the effect of scale on the strength and deformation properties of the rock mass is one of the most important issues. Prediction of uniaxial compressive strength in different diameters using the specimen size-effect models is valuable. To specify the application scope of the specimen size-effect models in the rock and concrete specimens, a few significant study have so far been carried out. This paper proposes a model of appropriate size-effect in sedimentary rocks and concrete specimens. Another object of this paper is discussion on the effect of specimen size and grain size on uniaxial compressive strength of rock and concrete specimens using statistical and experimental methods. The results of this study can be used for engineering designs in or on rocks and are more useful for determining of the elastic constants and compressive strength of rock.
 
Introduction
Dependence of compressive strength on the specimen size has a fundamental role in the designing of rock structures. In the rock mechanics, many experimental and analytical methods have been used to determine the specimen size-effect on the mechanical behavior of intact rock. In the area of rock mechanics and solid mechanics, the most notable proposed analytical models to predict the specimen size-effect on the uniaxial compressive strength are including the Weibull statistical theory (1951), the Hoek and Brown empirical theory (1980), the specimen size-effect model using fracture energy theory (Bazant, 1983 and 1984), the multi-fractal scaling model (Carpinteri et al., 1995), the fractal fracture size-effect model (Bazant, 1997) and the unified size-effect model for intact rock (Masoumi et al., 2015). To specify the application scope of these models in the rock and concrete specimens, few significant study have so far been carried out.
 
Methodology and Approaches
Statistical analysis of this study, were conducted in each size-effect model by means of a non-linear least-squares fitting algorithm and Levenberg-Marquardt method using SPSS software. In the experimental study, three concrete blocks of approximately 500mm×500mm×500mm in size with three different grain sizes (0-12, 0-20 and 0-25) were manufactured. After the curing time, using a laboratory drilling machine, cylindrical specimens were obtained from blocks with diameters of 56, 68, 72 and 94 mm and with a length-to-diameter ratio of 2.0 (L/D=2.0) according to the recommendation of International Society of Rock Mechanics (ISRM, 2007). ACI-211 standard and ASTM C33 standard were utilized for mixture design of samples and required grain sizes respectively.
 
Results and Conclusions
In the sedimentary rocks and concrete specimens, respectively, there was a good agreement between outputs of laboratory tests with the specimen size-effect model using fracture energy and the multifractal scaling model. In experimental study, results of uniaxial compressive strength tests for grain sizes 0-20 and 0-25 mm indicated that increase of the specimens' diameter resulted in first increase and then decrease of uniaxial compressive strength. The results of this study confirmed grain size effect on the predictions of specimen size-effect models (i.e. increase of the grain size, leads to reduction of the value of correlation coefficient for different models. These results can be used for engineering designs in rocks and concrete mixtures.

کلیدواژه‌ها [English]

  • Specimen Size-Effect
  • Grain Size Effect
  • Uniaxial Compressive Strength
  • Statistical Analysis
  • Fracture Energy
  • Elastic Constats
[1]           Masoumi, H., Douglas, K. J., & Russell, A. R. (2016). A bounding surface plasticity model for intact rock exhibiting size-dependent behavior. Rock Mech. Rock Eng., 49, 47-62.

[2]           Yoshinaka, R., Osada, M., Park, H., Sasaki, T., & Sasaki, K. (2008). Practical determination of mechanical design parameters of intact rock considering scale effect. Eng. Geol., 96(3–4), 173–186.

[3]           Poulsen, B. A., & Adhikary, D. P. (2013). A numerical study of the scale effect in coal strength. Int. J. Rock Mech. Min. Sci., 63, 62-71.

[4]           Masoumi, H., Saydam, S., & Hagan, P. C. (2015). Unified Size-Effect Law for Intact Rock. Int. J. Geomech., 16(2), 1-15.

[5]           Weibull, W. (1951). A statistical distribution of function of wide applicability. J. Appl. Mech., 18, 293–297.

[6]           Hoek, E., & Brown, E. T. (1980). Underground excavations in rock. Inst. Min. Metall., London, 527.

[7]           Bazant, Z. P., & ASCE, F. (1984). Size effect in blunt fracture: Concrete, rock, metal. J. Eng. Mech., 110(4), 518–535.

[8]           Carpinteri, A., Chiaia, B., & Ferro, G. (1995). Size effects on nominal tensile strength of concrete structures: multifractality of material ligaments and dimensional transition from order to disorder. Mater. Struct., 28(6), 311-317.

[9]           Bazant, Z. P. (1997). Scaling of quasibrittle fracture: Hypotheses of invasive and lacunar fractality, their critique and Weibull connection. Int. J. Frac., 83(1), 41-65.

[10]         Mogi, K. (1962). The influence of dimensions of specimens on the fracture strength of rocks. Bull. Earth Res. Inst., 40,175-185.

[11]         Baecher, G. B., & Einstein, H. H. (1981). Size effect in rock testing. Geophys. Res. Lett., 8(7), 671-674.

[12]         Thuro, K., Plinninger, R. J., Zah, S., & Schutz, S. (2001). Scale effects in rock strength properties. Part1: Unconfined compressive test and Brazilian test. Rock mechanics-a challenge for society, ISRM, Espoo, 169-174.

[13]         Pells, P. J. N. (2004). On the absence of size effects for substance strength of Hawkesbury Sandstone. Aust. Geomech., 39, 79-83.

[14]         Darlington, W. J., & Ranjith, P. G. (2011). The effect of specimen size on strength and other properties in laboratory testing of rock and rock-like cementitious brittle materials. Rock Mech. Rock Eng., 44(5), 513–529.

[15]         Bieniawski, Z. T. (1975). The point load test in geotechnical practice. Eng. Geol., 9, 1-11.

[16]         Greminger, M. (1982). Experimental studies of the influence of rock anisotropy and size and shape effects in point-load testing. Int. J. Rock Mech. Min. Sci., 19, 241-246.

[17]         Hawkins, A. B. (1998). Aspects of rock strength. Bull. Eng. Geol. Environ., 57, 17-30.

[18]         Thuro, K., Plinninger, R. J., Zah, S., & Schutz, S. (2001b). Scale effect in rock strength properties. Part 2: Point load test and point load strength index. In Rock Mechanics- a challenge for Society, Zeitlinger, Switzerland, 175-180.

[19]         Forbes, M., Masoumi, H., Saydam, S., & Hagan, P. (2015). Investigation into the effect of length to diameter ratio on the point load strength index of Gosford sandstone. In 49th U.S. Rock Mechanics/Geomechanics Symp., American Rock Mechanics Association, San Francisco.

[20]         Andreev, G. E. (1991a). A review of the Brazilian test for rock tensile strength determination. Part I: Calculation formula. Min. Sci. Tech., 13(3), 445-456.

[21]         Andreev, G. E. (1991b). A review of the Brazilian test for rock tensile strength determination. Part II: Contact conditions. Min. Sci. Tech., 13(3), 457-465.

[22]         Butenuth, C. (1997). Comparison of tensile strength values of rocks determined by point load and direct tension tests. Rock Mech. Rock Eng., 30(1), 65-72.

[23]         Elices, M., & Rocco, C. (1999). Size effect and boundary conditions in Brazilian test: Theoretical analysis. Mater. Struct., 32(6), 437-444.

[24]         Çanakci, H., & Pala, M. (2007). Tensile strength of basalt from a neural network. Eng. Geol., 94(1-2), 10-18.

[25]          Singh, M. M., & Huck, P. J. (1972). Large scale triaxial tests on rock. In the 14th US Symp. on Rock Mech., Pennsylvania State Univ., 35-60.

[26]         Hunt, D. D. (1973). The Influence of Confining Pressure on Size Effect. Master of Science, Massachusetts Institute of Technology, Cambridge.

[27]         Medhurst, T. P., & Brown, E. T. (1998). A study of the mechanical behaviour of coal for pillar design. Int. J. Rock Mech. Min. Sci., 35(8), 1087-1105.

[28]         Aubertin, M., Li, L., & Simon, R. (2000). A multiaxial stress criterion for short and long term strength of isotropic rock media. Int. J. Rock Mech. Min. Sci., 37(8), 1169-1193.

[29]         Masoumi, H., Roshan, H., & Hagan, P. C. (2016). Size-dependent Hoek-Brown failure criterion. Int. J. Geomech., 17(2), 1-12.

[30]         Weibull, W. (1939). A statistical theory of the strength of materials. Ingeniors Vetenskaps Akademiens Handlingar, 151, 1-29.

[31]         Bieniawski, Z. T. (1968). The effect of specimen size on compressive strength of coal. Int. J. Rock Mech. Min. Sci., 5, 325-335.

[32]         Pretorius, J. P. G., & Se, M. (1972). Weakness correlation and the size effect in rock strength tests. JS Afr. Inst. Min. Met., 12, 322-327.

[33]         Bazant, Z. P., & Oh, B. H. (1983). Crack band theory for fracture of concrete. Mater. Struct., 16, 155-177.

[34]         Bazant, Z. P., & Chen, E. P. (1997). Scaling of structural failure. Appl. Mech. Rev., 50(10), 593-627.

[35]         Bazant, Z. P., & Planas, J. (1998). Fracture and Size Effect in Concrete and Other Quasibrittle Materials. CRC Press.

[36]         Griffith, A. A. (1924). The theory of rupture. In 1st Int. Congress of Applied Mech., Delft, Netherlands, 55-63.

[37]         Adey, R. A., & Pusch, R. (1999). Scale dependency in rock strength. Eng. Geol., 53, 251-258.

[38]         Bazant, Z. P., Lin, F. B., & Lippmann, H. (1993). Fracture energy release and size effect in borehole breakout. Int. J. Numer. Anal. Methods Geomech., 17, 1-14.

[39]         Carpinteri, A. (1994). Fractal nature of material microstructure and size effects on apparent mechanical properties. Mech. Mater., 18, 89-101.

[40]         Carpinteri, A., & Mainardi, F. (1997). Fractals and Fractional Calculus in Continuum Mechanics. Springer.

[41]         Yuki, N., Aoto, S., Yoshinaka, R., Yoshihiro, O., & Terada, M. (1995). The scale and creep effect on the strength of welded tuff. In Int. Workshop on Rock Foundation, Balkema, Tokyo.

[42]         Hoek, E. (2000). Rock Engineering Course Notes by Evert Hoek.

[43]         Bazant, Z. P., & et al. (2004). RILEM TC QFS, Quasibrittle fracture scaling and size effect-Final report. Mater. Struct., 37, 547-568.

[44]         Ovalle, C., Frossard, E., Dano, C.,  Hu, W., Maiolino, S., & Hicher, P. Y. (2014). The effect of size on the strength of coarse rock aggregates and large rockfill samples through experimental data. Acta Mech., 225, 2199-2216.

[45]         Zhang, Q., Zhu, H., Zhang, L., & Ding, X. (2011). Study of scale effect on intact rock strength using particle flow modeling. Int. J. Rock Mech. Min. Sci., 48, 1320-1328.

[46]         Bazant, Z. P., & Xi, Y. (1991). Statistical size effect in quasi-brittle structures: II. Nonlocal theory. ASCE J. Eng. Mech., 117(11), 2623-2640.

[47]         Carpinteri, A., Ferro, G., & Monetto, I. (1999). Scale effects in uniaxially compressed concrete Specimens. Mag. Concr. Res., 51(3), 217-225.

[48]         Natau, O., Frolich, B. O., & Mutschler, T. O. (1983). Recent development of the large scale triaxial test.  In ISRM Congress, Melbourne, A65-A74.

[49]         Hoskins, J. R., & Horino, F. G. (1969). Influence of Spherical Head Size and Specimen Diameters on the Uniaxial Compressive Strength of Rocks. US Department of the Interior, Bureau of Mines, Washington.

[50]         Vutukuri, V. S., Lama, R. D., & Saluja, S. S. (1978). Handbook on Mechanical Properties of Rocks, Trans. Tech. Publications.

[51]         Blanks, R. F., & Mcnamara, C. C. (1935). Mass concrete tests in large cylinders. J. Am. Concrete Inst., 31, 280-303.

[52]         ISRM. (2007). The Complete ISRM Suggested Methods for Rock Characterization, Testing and Monitoring: 1974-2006. Ulusay, R., & Hudson, J. A. (eds.), Suggested Methods Prepared by the Commission on Testing Methods, International Society for Rock Mechanics, Compilation Arranged by the ISRM Turkish National Group, Ankara, Turkey.

[53]         Rezaee, H. (2015). Experimental Evaluation of the Effect of Specimen and Grain Size on the Mechanical Properties and Fracture Behavior of Rock, MSc Thesis, Isfahan University of Technology.

[54]          ACI (American Concrete Institute). (1988). Measurement of Properties of Fiber Reinforced Concrete. 85(6), 583-593.

[55]          ASTM. (2003). Standard Specification for Concrete Aggregates- C33-03. Annual Book of ASTM Standards, 4(2).