Skip to main content
SpringerLink
Log in

Coalescence of Fractures Under Uni-axial Compression and Fatigue Loading

  • Original Paper
  • Published:
Rock Mechanics and Rock Engineering Aims and scope Submit manuscript

Abstract

In this paper, white Portland cement was used as an experimental material. Prismatic specimens with pre-existing flaws at different angles of inclination (α) varying through 0°, 30°, 45°, 60°, 75° to 90° and cylindrical specimens with different numbers of pre-existing flaws (n) varying through 0, 1, 2 to 3 were tested under uni-axial compression tests. Crack initiation, propagation, coalescence, and failure were observed. The corresponding analytical expression for the stress intensity factor under uni-axial compression was derived, the coefficient of friction and the stress intensity factor of the specimens on the surfaces of the crack were analysed, and the corrective coefficient for the stress intensity factor was introduced. Fatigue tests with a loading frequency of f = 100 Hz were carried out on cylindrical specimens with constant amplitude of the cyclic load which is a proportion of the compressive load at failure (F f) obtained from the uni-axial compression tests. The fatigue property of the specimens was analysed and the relationship (S max − lg N f) between the maximum stress and the number of loading cycles at failure for specimens with pre-existing flaws was proposed. The effect of pre-existing flaws on the fatigue life (N f) and dynamic load (S D) which can be applied was investigated.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

Abbreviations

a :

Half the flaw length (mm)

a 0 :

Initial half the flaw length (mm)

b :

Vertical space (mm)

f :

Cyclic loading frequency (Hz)

F f :

Load at failure (kN)

F N :

Corrective coefficient of the stress intensity factor

h :

Horizontal space (mm)

k II :

Stress intensity factor for type II pure shear flaw \( \left( {{\text{MPa}}\sqrt {\text{mm}} } \right) \)

n :

Number of pre-existing flaws

N f :

Number of loading cycles at failure

S D :

Dynamic load (kN)

S DS :

Static load (kN)

S max :

Maximum load (kN)

T :

Test period (min)

w :

Width of the specimen (mm)

α :

Inclination angle of the flaw (°)

μ f :

Coefficient of friction

σ 1 :

Compressive stress (MPa)

σ 1f :

Compressive stress at failure (MPa)

σ α :

Normal stress (MPa)

τ α :

Shear stress (MPa)

τ r :

Resultant shear stress (MPa)

References

  • Badge MN, Petroš V (2005) Waveform effect on fatigue properties of intact sandstone in uniaxial cyclical loading. Rock Mech Rock Eng 38(3):169–196

    Article  Google Scholar 

  • Bobet A, Einstein HH (1998) Fracture coalescence in rock-type materials under uniaxial and biaxial compression. Int J Rock Mech Min Sci 35(7):863–888

    Article  Google Scholar 

  • Horii H, Nasser S (1985) Compression-induced microcrack growth in brittle solids: axial splitting and shear failure. J Geophys Res 90(B4):3105–3125

    Article  Google Scholar 

  • Ko TY, Kemeny J (2008a) Experimental study of subcritical crack growth under mode I, mode II and mode III loading. In: Proceedings of the 42nd US Rock Mechanics Symposium and 2nd US-Canada Rock Mechanics Symposium, paper 928, Am. Rock Mech. Assoc., Washington, DC

  • Ko TY, Kemeny J (2008b) Size effect on subcritical crack growth in Coconino sandstone. In: Proceedings of the 42nd US Rock Mechanics Symposium and 2nd US-Canada Rock Mechanics Symposium, paper 055, Am. Rock Mech. Assoc., Washington, DC

  • Ko TY, Kemeny J (2011) Subcritical crack growth in rocks under shear loading. J Geophys Res 116:B01407. doi:10.1029/2010JB000846

    Article  Google Scholar 

  • Lajtai EZ, Schmidtke RH (1986) Delayed failure in rock loaded in uniaxial compression. Rock Mech Rock Eng 19:11–25

    Article  Google Scholar 

  • Liu HY, Kou SQ, Lindqvist P–A, Tang CA (2007) Numerical modelling of the heterogeneous rock fracture process using various test techniques. Rock Mech Rock Eng 40(2):107–144

    Article  Google Scholar 

  • Moelle KHR, Li G, Lewis JA (1990) On fatigue crack development in some anisotropic sedimentary rocks. Eng Fract Mech 35(1–3):367–376

    Article  Google Scholar 

  • Rao MVMS, Ramana YV (1992) A study of progressive failure of rock under cyclic loading by ultrasonic and AE monitoring techniques. Rock Mech Rock Eng 25(4):237–251

    Article  Google Scholar 

  • Reyes O, Einstein HH (1992) Fracture mechanics of fractured rock. Int J Rock Mech Min Sci 29(4):217–224

    Google Scholar 

  • Shan YF, Luo RA, Song XY, Cheng CJ (2003) Application of ZWICK2100 high-frequency vibration testing machine in the research of rock mechanical property. Rock Soil Mech 24(Suppl 2):171–174 (in Chinese)

    Google Scholar 

  • Shen B, Stephansson O, Einstein HH (1995) Coalescence of fractures under shear stresses in experiments. J Geophys Res 100(B4):5975–5990

    Article  Google Scholar 

  • Singh SK (1988) Relationship among fatigue strength, mean grain size and compressive strength of a rock. Rock Mech Rock Eng 21:271–276

    Article  Google Scholar 

  • Wong RHC, Chau KT (1998) Crack coalescence in a rock-like material containing two cracks. Int J Rock Mech Min Sci 35(3):147–161

    Google Scholar 

  • Wong LNY, Einstein HH (2009a) Crack coalescence in molded gypsum and carrara marble: Part 1. Macroscopic observations. Rock Mech Rock Eng 42:475–511

    Article  Google Scholar 

  • Wong LNY, Einstein HH (2009b) Crack coalescence in molded gypsum and carrara marble: Part 2. Microscopic observations and interpretation. Rock Mech Rock Eng 42:513–545

    Article  Google Scholar 

  • Yang H, Cao P, Jiang XL, Huang SA, Li ZC, Xu MQ (2008) Analytical and numerical research of stress intensity factor with a closed-crack in finite-rock-plate under biaxial compression. J Cent South Univ (Sci Technol) 39(4):850–855 (in Chinese)

    Google Scholar 

  • Zhou SZ, Dang FN, Chen HQ, Long Q (2008) Numerical method for crack extension analysis based on fatigue fracture process of rock materials. Rock Soil Mech 29(3):699–774 (in Chinese)

    Google Scholar 

Download references

Acknowledgments

The financial support from National Natural Science Foundation of China (10872133, 11010101024), Shanghai Pujiang Talent Program, Key Innovation Program of Shanghai Municipal Education Commission for this study is gratefully acknowledged.

Author information

Authors and Affiliations

  1. Department of Civil Engineering, University of Shanghai for Science and Technology, 516 Jungong Road, Shanghai, 200093, People’s Republic of China

    Y. L. Chen, J. Ni, W. Shao & Y. C. Zhou

  2. Department of Engineering, University of Exeter, North Park Road, Exeter, EX4 4QF, UK

    A. Javadi

  3. Department of Engineering Geology and Hydrogeology, RWTH Aachen University, Lochnerstr. 4-20, 52064, Aachen, Germany

    R. Azzam

Authors
  1. Y. L. Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Ni
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. W. Shao
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Y. C. Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. A. Javadi
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. R. Azzam
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. Ni.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chen, Y.L., Ni, J., Shao, W. et al. Coalescence of Fractures Under Uni-axial Compression and Fatigue Loading. Rock Mech Rock Eng 45, 241–249 (2012). https://doi.org/10.1007/s00603-011-0186-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00603-011-0186-x

Keywords

Search

Navigation