• Tunnel and Underground Space
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• v.29 no.2
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• pp.124-134
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• 2019

Subcritical crack growth in rock material can occur under monotonic and cyclic loading. Subcritical crack growth plays an important role in evaluating the long-term stability of structures in rocks. This paper presents the results of studies conducted to determine subcritical crack growth parameters under monotonic and cyclic loading in rock-like material. The constant stress rate method was employed for monotonic loading. The subcritical crack growth parameter of n under cyclic loading was determined by the relation between the rate of crack growth per cycle and stress intensity factor range. The specimens contained pre-existing flaws with 45 and 60 degrees of inclination angle and flaws spacing and continuity were varied to arrange crack growth in shear or tensile manner. The results show that the parameter of n is almost constant regardless of the applied load conditions such as monotonic and cyclic or shear and tension.

• Tunnel and Underground Space
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• v.19 no.2
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• pp.95-106
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• 2009

Numerical analysis of the progressive failure of a rock slope was conducted using a 3-D rock joint element considering fracture mechanics and subcritical crack growth of asperities in the rock joints. Even though the stress state in the rock slope is not changing, the elapse of time causes subcritical crack growth to break asperities in the joints. The increase of broken asperities causes failure of joints in the rock slope and the increase of failed joints results in failure of a jointed rock slope. As a result, the progressive failure of a jointed rock slope due to the gradual breaking of small asperities along joints generated by subcritical crack growth occurs at a lower stress than if rock failure occurred by exceeding the static strength or fracture toughness.

• Geophysics and Geophysical Exploration
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• v.12 no.1
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• pp.163-171
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• 2009

Subcritical crack growth is one of the main causes of time-dependent fracturing in rock. In the present study, we investigated subcritical crack growth in rock in distilled water (pH = 5.7) and in an aqueous solution of sodium hydroxide (NaOHaq, pH = 12), comparing the results to those in air. We also investigated the effect of the pH in an aqueous environment. We used andesite and granite for all our tests. We determined the relationship between the crack velocity and the stress intensity factor using the double-torsion test under conditions of controlled temperature. We showed that crack velocities in water were higher than those in air, in agreement with other research results indicating that crack velocity increases in water. When we compared our results for NaOHaq with those for water, however, we found that the crack velocity at the same stress intensity factor did not change even though the pH of the surrounding environment was different. This result does not agree with the accepted understanding that hydroxide ions accelerate subcritical crack growth in rocks. We concluded that the pH at the crack tip influences subcritical crack growth, and not the bulk pH, which has little effect.

• Tunnel and Underground Space
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• v.19 no.2
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• pp.86-94
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• 2009

A three dimensional rock joint element was developed considering fracture mechanics and subcritical crack growth to simulate non-linear behavior and the progressive failure of rock joints. Using this 3-D joint element, joint shear tests of rock discontinuities were simulated by a numerical method. The asperities on the joint surface began to fail at stress levels lower than the rock fracture toughness and continued progressively due to subcritical crack growth. As a result of progressive failing in each and every asperity, the joint showed non-linear stress-time behavior including stress hardening/softening and the reaching of a residual stress.

• Journal of the Korean Mathematical Society
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• v.53 no.2
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• pp.247-262
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• 2016

In this paper, we consider the following $Schr{\ddot{o}}dinger$-Poisson system: $$\{\begin{array}{lll}-{\Delta}u+u+{\lambda}{\phi}u={\mu}f(u)+{\mid}u{\mid}^{p-2}u,\;\text{ in }{\Omega},\\-{\Delta}{\phi}=u^2,\;\text{ in }{\Omega},\\{\phi}=u=0,\;\text{ on }{\partial}{\Omega},\end{array}$$ where ${\Omega}$ is a smooth and bounded domain in $\mathbb{R}^3$, $p{\in}(1,6]$, ${\lambda}$, ${\mu}$ are two parameters and $f:\mathbb{R}{\rightarrow}\mathbb{R}$ is a continuous function. Using some critical point theorems and truncation technique, we obtain three multiplicity results for such a problem with subcritical or critical growth.

• Journal of the Korean Ceramic Society
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• v.22 no.4
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• pp.26-32
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• 1985

The subcritical crack growth of sintered SiC is investigated under various corrosive atmospheres such as distilled water Murakami solution and saturated KOH solution. The KI-V diagrams are obtained by the load relaxation method and incremental displacement rate method using the double torsion technique. The obtained fracture mechanics parameters (n) of sintered SiC are 79 in Murakami solution and 39 in saturated KOH solution. These data indicate that the subcritical crack growth of sintered SiC is taking place in these two conditions and the stress-corrosion cracking is suggested to be the mechanism. With these KI-V diagrams the life of sintered SiC in these conditions is predicted.

• Bulletin of the Korean Mathematical Society
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• v.54 no.3
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• pp.1023-1036
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• 2017

In this paper, we study the existence of positive solutions to the p-Kirchhoff elliptic equation involving general subcritical growth $(a+{\lambda}{\int_{\mathbb{R}^N}{\mid}{\nabla}u{\mid}^pdx+{\lambda}b{\int_{\mathbb{R}^N}{\mid}u{\mid}^pdx)(-{\Delta}_pu+b{\mid}u{\mid}^{p-2}u)=h(u)$, in ${\mathbb{R}}^N$, where a, b > 0, ${\lambda}$ is a parameter and the nonlinearity h(s) satisfies the weaker conditions than the ones in our known literature. We also consider the asymptotics of solutions with respect to the parameter ${\lambda}$.

• Tunnel and Underground Space
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• v.24 no.1
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• pp.67-80
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• 2014

Long-term stability and delayed failure of granite were evaluated through the laboratory test based on Wilkins method and Brazilian disc test (BDT) which yields tensile strength, mode I fracture toughness and subcritical crack growth parameters. Then, the long-term strength of granite was estimated by using analytical models and long-term stability of compressed air-energy storage (CAES) pilot cavern pressurized up to 5 ~ 6 MPa was evaluated using numerical code, FRACOD with the determined subcritical crack growth parameters. The results of test and analyses showed that the subcritical crack growth index, n was determined as 29.39 and the inner pressure of 5 ~ 6 MPa had an insignificant effect on the long-term stability of pilot cavern. It was also found that the measurement and analysis of acoustic emission events can describe the accumulation of damage due to subcritical crack growth quantitatively. That is, AE monitoring can provide the current status of rock under loading if we make an identical installation condition in the field with that of the laboratory test.

• Journal of the Korean Ceramic Society
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• v.33 no.2
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• pp.203-213
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• 1996

In this study the subcritical crack growth behavior in an Al2O3-SiCw composite has been investigated using in situ fracture technique of applied moment double cantilever beam (AMDCB) specimens indside an SEM. This technique allows the detailed observation of whisker and grain bridging in the crack wake region. The experimental results indicated that the KI-a curve was deviated from the conventional powder law form and that the existed a region where the rate of microcrack growth was decreased with increasing the externally applied stress intensity factor. This behavior could be explained by arising crack growth resistance i.e. R-curve behavior which was associated with crack shielding due to whisker and grain bridging. The R-curve was also analyzed from the KI-a curve data in order to quantify the bridging effect in the Al2O3-SiCw composite.

• Korean Journal of Mathematics
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• v.19 no.4
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• pp.423-436
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• 2011

We obtain a theorem that shows the existence of multiple solutions for the mixed type nonlinear elliptic equation with Dirichlet boundary condition. Here the nonlinear part contain the jumping nonlinearity and the subcritical growth nonlinearity. We first show the existence of a positive solution and next find the second nontrivial solution by applying the variational method and the mountain pass method in the critical point theory. By investigating that the functional I satisfies the mountain pass geometry we show the existence of at least two nontrivial solutions for the equation.