Mechanical Responses and Damage Model of Anchored Jointed Rock Mass under Fatigue Shear Load
Publication: International Journal of Geomechanics
Volume 23, Issue 3
Abstract
Cyclical impact loads will transform into low-frequency fatigue loads during propagation and will induce creep deformation of far-field rock under long-term disturbance loads. Laboratory tests of specimens under different fatigue shear loads were conducted. The mechanical responses and creep laws of the specimen were analyzed in detail. Based on the experimental results, a new constitutive model was explored. The results reveal that the stress‒strain curves of the specimen show a trend of step-path increasing under stable and fatigue load circularly. With an increase in fatigue load, the shear strength and elastic modulus of the specimens decrease gradually, while the corresponding failure strain increases gradually. The damage index composed of peak time and peak shear stress can reflect the failure of rock under fatigue loading, and the fatigue amplitude has the greatest influence on specimen deterioration. A fatigue stage in the shear creep curve occurs and is caused by the fatigue load. The fatigue creep rate increases gradually as the fatigue parameter increases. A combined nonlinear damage creep model based on the Nishihara model, elastic body, nonlinear creep body, and fatigue damage function (termed the NENF model), describing the creep responses of rock, anchor, accelerated creep, and fatigue load, respectively, was established. Compared with test data, the creep equation of the model has good accuracy in describing the whole shear creep process of specimens under fatigue loading and provides a new framework for the stability of anchoring rock masses.
Practical Applications
In this study, an experimental study on the mechanical responses of marble under different fatigue loads was conducted using a servo-controlled compression shear test machine equipped with an improved fixture system. The mechanical responses and creep laws of the specimen were analyzed in great detail. Based on the experimental results, a combined Nishihara model, elastic body, nonlinear creep body, and fatigue damage function (NENF) model describing the whole process of shear creep in an anchored joint rock mass (AJRM) under fatigue load was established. Compared with test data, the creep equation of the model has a good accuracy in describing the whole shear creep process of the specimen under the combination of stable load and fatigue load. This study provides the theoretical basis for the understanding of the long-term stability in AJRM.
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Acknowledgments
This work is supported by the National Natural Science Foundation of China (Nos. 42277187 and 41972297) and the Natural Science Foundation of Hebei Province (No. D2021202002).
Notation
The following symbols are used in this paper:
- Ar
- area of AJRM;
- As
- area of the anchor;
- a1
- material parameter;
- a2
- material parameter;
- bi (i = 1, 2, …, 9)
- equation parameters;
- ci (i = 1, 2, 3)
- equation parameters;
- D
- damage factor;
- D[V(x)]
- fatigue damage function of the specimen;
- Du
- ultimate damage, Du = 1;
- E
- elastic modulus;
- f
- fatigue frequency;
- FA
- fatigue amplitude;
- Faf
- adhesion force between filling and mineral;
- Fam
- adhesion force between minerals;
- Fe
- extrusion force;
- Ff
- fatigue load;
- Fff
- friction force between filling and mineral;
- Ffm
- friction force between minerals;
- Fi
- interaction force;
- Fs
- stable force;
- Ft
- tensile force;
- G0
- actual shear modulus;
- G4
- parameters of the nonlinear creep body;
- Gi (i = 1, 2, 3)
- shear modulus;
- Md
- damage index;
- N
- fatigue cycle number;
- n
- parameters of the nonlinear creep body;
- Q
- iteration number;
- Qi
- initial number of iterations;
- R2
- fitting parameters;
- Rf
- fatigue creep rate;
- t1
- critical damage time;
- t2
- start time of steady state;
- t3
- start time of acceleration state;
- t4
- failure time;
- tA
- time before the fatigue load is applied;
- tB
- time after the fatigue load is applied;
- tp
- peak time;
- V
- pore volume fraction;
- V(x)
- function of pore volume fraction under fatigue load;
- x
- fatigue load;
- ɛ
- strain;
- γA
- shear strain before the fatigue load is applied;
- γB
- shear strain after the fatigue load is applied;
- γc
- shear strain of the coupling model;
- γe
- shear strain of the elastic body;
- γef
- effective shear strain;
- γf
- failure strain;
- γH
- total strain under high shear stress;
- γH0
- instantaneous strain under high shear stress;
- γHA
- accelerate strain under high shear stress;
- γHa
- attenuation strain under high shear stress;
- γHf
- fatigue strain under high shear stress;
- γHs
- steady strain under high shear stress;
- γL
- total strain under low shear stress;
- γL0
- instantaneous strain under low shear stress;
- γLa
- attenuation strain under low shear stress;
- γLf
- fatigue strain under low shear stress;
- γN
- shear strain of the Nishihara model;
- γnc
- shear strain of the nonlinear creep body;
- γw
- shear strain of the whole process under stable load;
- γwef
- shear strain of the whole process under fatigue load;
- γ0
- apparent shear strain;
- η1
- viscosity coefficient;
- σ
- stress;
- σc
- complete fatigue stress;
- σn
- undisturbed stress;
- σo
- apparent stress;
- τc
- shear stress of the coupling model;
- τe
- shear stress of elastic body;
- τn
- const;
- τN
- shear stress of the Nishihara model;
- τp
- peak shear strength;
- τs
- long-term strength;
- τ0
- initial shear stress;
- τ1
- critical damage shear stress;
- τ2
- start shear stress of steady state;
- τ3
- start shear stress of acceleration state; and
- τ4
- failure shear stress.
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Published In
International Journal of Geomechanics
Volume 23 • Issue 3 • March 2023
Copyright
© 2022 American Society of Civil Engineers.
History
Received: May 13, 2022
Accepted: Sep 13, 2022
Published online: Dec 21, 2022
Published in print: Mar 1, 2023
Discussion open until: May 21, 2023
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