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Mixed-Mode Fracture Behavior and Related Surface Topography Feature of a Typical Sandstone

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Abstract

The geo-mechanical properties of reservoirs, especially the morphology of the rock surface and the fracture properties of rocks, are of great importance in the modeling and simulation of hydraulic processes. To better understand these fundamental issues, five groups of mixed-mode fracture tests were conducted on sandstone using edge-cracked semi-circular bend specimens. Accordingly, the fracture loads, growth paths and fracture surfaces for different initial mixities of the mixed-mode loadings from pure mode I to pure mode II were then determined. A surface topography measurement for each rough fracture surface was conducted using a laser profilometer, and the fractal properties of these surfaces were then investigated. The fracture path evolution mechanism was also investigated via optical microscopy. Moreover, the mixed-mode fracture strength envelope and the crack propagation trajectories of sandstone were theoretically modeled using three widely accepted fracture criteria (i.e., the MTS, MSED and MERR criterions). The published test results in Hasanpour and Choupani (World Acad Sci Eng Tech 41:764–769, 2008) for limestone were also theoretically investigated to further examine the effectiveness of the above fracture criteria. However, none of these criteria could accurately predict the fracture envelopes of both sandstone and limestone. To better estimate the fracture strength of mixed-mode fractures, an empirical maximum tensile stress (EMTS) criterion was proposed and found to achieve good agreement with the test results. Finally, a uniformly pressurized fracture model was simulated for low pressurization rates using this criterion.

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Abbreviations

a :

Crack length

B :

Thickness of an SCB specimen

d :

Half-distance of two bottom supports of an SCB specimen

E :

Young’s modulus

f :

Coefficient of friction

F :

Applied load in an SCB 3PB test

F max :

Peak load in an SCB 3PB test

G :

Energy release rate

G c :

Critical energy release rate

K I :

Mode I stress intensity factor

K II :

Mode II stress intensity factor

K Ic :

Mode I fracture toughness

K IIc :

Mode II fracture toughness

k 1 :

=K I/K Ic

k 2 :

=K II/K IIc

M :

Mixity of a given mixed-mode loading

M 0 :

Initial loading mode mixity

p :

Pressure acting on the wellbore and the fracture surfaces

p i :

Pressure acting on the wellbore and the fracture surfaces for sub-step i

R :

Radius of an SCB specimen

r, θ :

Polar co-ordinates at the crack tip

r c :

Critical radius of the core region in the crack initiation direction

r Ic :

Critical radius of the core region in the initiation direction of a mode I crack

r IIc :

Radius of the core region in the initiation direction of a mode II crack

R w :

Radius of a wellbore

S :

Strain energy density factor

S c :

Critical strain energy density factor

T :

Nonsingular term stress

Y I :

Non-dimensional mode I stress intensity factor

Y II :

Non-dimensional mode II stress intensity factor

α I, α II :

Magnitude parameters of a mixed-mode loading

β :

Crack inclined angle for an SCB specimen

θ 0 :

Crack initiation angle

κ :

=3 − 4ν for plain strain, =(3 − ν)/(1+ν) for plain stress

λ :

An empirical coefficient calculated from (r c/r Ic)1/2

μ :

Modulus of rigidity

ν :

Poisson’s ratio

σ h :

Far-field in-plane minimum principal stress

σ H :

Far-field in-plane maximum principal stress

σ n :

Normal stress acting on the fracture surfaces

σ θθ :

Tangential stress ahead of a crack

σ θθc :

Critical tangential stress

φ :

Normalized dimensionless parameter that controls the fracture path

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Acknowledgments

The authors would like to thank Prof. Qizhi Wang of Sichuan University for his kind help. This work was financially supported by the Provincial Science and Technology Support Project of Sichuan Province (2012FZ0124) and the Major State Basic Research Project of NSFC (2011CB201201).

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Authors and Affiliations

  1. Key Laboratory of Energy Engineering Safety and Disaster Mechanics, Sichuan University, Chengdu, 610065, China

    L. Ren, L. Z. Xie, H. P. Xie, T. Ai & B. He

  2. School of Architecture and Environment, Sichuan University, Chengdu, 610065, China

    L. Ren, H. P. Xie & T. Ai

  3. Institute of New Energy and Low-Carbon Technology, Sichuan University, Chengdu, 610065, China

    L. Z. Xie & B. He

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  1. L. Ren
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Ren, L., Xie, L.Z., Xie, H.P. et al. Mixed-Mode Fracture Behavior and Related Surface Topography Feature of a Typical Sandstone. Rock Mech Rock Eng 49, 3137–3153 (2016). https://doi.org/10.1007/s00603-016-0959-3

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