Rock Mechanics and Rock Engineering

, Volume 49, Issue 12, pp 4681–4698 | Cite as

Estimation Criteria for Rock Brittleness Based on Energy Analysis During the Rupturing Process

Original Paper


Brittleness is one of the most important mechanical properties of rock: it plays a significant role in evaluating the risk of rock bursts and in analysis of borehole-wall stability during shale gas development. Brittleness is also a critical parameter in the design of hydraulic fracturing. However, there is still no widely accepted definition of the concept of brittleness in rock mechanics. Although many criteria have been proposed to characterize rock brittleness, their applicability and reliability have yet to be verified. In this paper, the brittleness of rock under compression is defined as the ability of a rock to accumulate elastic energy during the pre-peak stage and to self-sustain fracture propagation in the post-peak stage. This ability is related to three types of energy: fracture energy, post-peak released energy and pre-peak dissipation energy. New brittleness evaluation indices B 1 and B 2 are proposed based on the stress–strain curve from the viewpoint of energy. The new indices can describe the entire transition of rock from absolute plasticity to absolute brittleness. In addition, the brittle characteristics reflected by other brittleness indices can be described, and the calculation results of B 1 and B 2 are continuous and monotonic. Triaxial compression tests on different types of rock were carried out under different confining pressures. Based on B 1 and B 2, the brittleness of different rocks shows different trends with rising confining pressure. The brittleness of red sandstone decreases with increasing confining pressure, whereas for black shale it initially increases and then decreases in a certain range of confining pressure. Granite displays a constant increasing trend. The brittleness anisotropy of black shale is discussed. The smaller the angle between the loading direction and the bedding plane, the greater the brittleness. The calculation B 1 and B 2 requires experimental data, and the values of these two indices represent only relative brittleness under certain conditions. In field operations, both the relative brittleness and the brittleness obtained from seismic data or mineral composition should be considered to gain a more comprehensive knowledge of the brittleness of rock material.


Brittleness Type II rock behavior Fracture mechanism Energy change Anisotropy of brittleness 

List of Symbols

VQuartz, VCarbonate, VClay

The content of quartz, carbonate and clay content, respectively (Eq. 1)


The weight coefficient of each mineral (Eq. 2)


The types of brittle minerals (Eq. 2)


The types of all minerals (Eq. 2)


The mineral content (volume fraction) (Eq. 2)

σc, σt

Uniaxial compressive strength and tensile strength of rock material (Eq. 3)


Initiation stress of rock material (Eq. 4)

E, v

The elastic modulus and Poisson’s ratio based on the seismic data (Eq.5)

Emax, Emin

The maximum and minimum values of the Elastic modulus (Eq. 5)

vmax, vmin

The maximum and minimum values of the Poisson’s ratio (Eq. 5)

εel, εpl

The elastic strain and plastic strain at the pre-peak stage of stress–strain curves (Eq. 6)


Total strain of pre-peak stage (Eq. 6)

σp, σr

The peak strength and the residual strength of the whole stress–strain curve (Eq. 7)

εp, εr

The peak strain and the residual strain of the whole stress–strain curve (Eq. 7)


The fracture energy (Eq. 8)


The unloading elastic energy (Eq. 8)


The dissipation energy of pre-peak stage (Eq. 8)


The extra energy required (type I behavior) or the excess energy released(type II behavior) (Eq. 9)


The total elastic energy accumulated in the rock specimen when reaching the peak strength (Eq. 10)


The energy which unconsumed or converts into other forms (Eq. 10)


The peak strength of the rock specimen under compression (Eq. 10)


The residual strength; σ i represents the function of pre-peak curve (Eq. 10)


Elastic modulus of stress–strain curve (Eq. 11)


Post-peak modulus of stress–strain curve (Eq. 11)


The function of pre-peak curve (Eq. 13)


The strain corresponding to the peak strength (Eq. 13)



The research was supported by Natural Science for Youth Foundation of China (No. 51504068).


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Copyright information

© Springer-Verlag Wien 2016

Authors and Affiliations

  1. 1.Department of Petroleum EngineeringNortheast Petroleum UniversityDaqingChina

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