Moment tensor analysis of acoustic emission for cracking mechanisms in rock with a pre-cut circular hole under uniaxial compression
Introduction
Acoustic Emissions (AE) technique can continuously monitor the spatial–temporal evolution of micro-cracks and, thus, may reveal the deformation processes as well as the failure mechanisms in rocks under loading. Pioneering works of the AE studies on rocks were performed by Mogi [1] and Scholz [2]. Following these works, a series of achievements has been realized, e.g., the AE location algorithms, the temporal–spatial evolution behaviors of micro-cracks in rock bodies and the change of the AE parameters during rock fracture process [3], [4], [5], [6], [7], [8], [9]. In the study of rock mechanics, it is not sufficient only to know where the micro-cracks take place. The deep understanding on the development and propagation of the micro-cracks requires knowledge of their fracture modes. The realization of this objective becomes possible using analysis method of moment tensor (MT) theory. MT inversion is a quite useful and quantitative approach for AE source analysis. In 1971, Gilbert [10] introduced for the first time the concept of the MT in the study of rock failure process. Aki and Richards [11] proposed the eigenvalue formulas of the MT for shear-mode fracture and tensile-mode fracture. Ohtsu [12], [13] presented the details of the MT theory for determining the direction, the mode and the volume of cracks, and developed a software package called Simplified Green’s Function for Moment Tensor Analysis, SiGMA. Chang and Lee [14] determined that the micro-cracks within a rock under triaxial compression are primarily shear cracks, and their proportions were augmented along with the increase of the confining pressures. Lei et al. [15] found that in coarse-grained granite samples, the overall failure process was dominated by shear cracks, while in fine-grained granite samples tensile cracks dominated in stress states below 80% of the peak stress that was beyond the stress limit at which shear cracks started increasing progressively. Based on the tests of hydro-fracturing with the use of AE techniques, Manthei et al. [16] considered that the directions of the macroscopic fracture surfaces coincide with those of the micro-crack directions according to the MT analysis. In the studies performed by Graham et al. [17] and Charalampidou et al. [18], the polarity method and the MT analysis could both provide similar results in terms of the AE source mechanisms, depending on the classification of the micro-crack types.
Although many significant studies have been performed on the fracturing mechanism of micro-cracks using the MT theory, these studies investigated mainly for solid specimens. In underground engineering structures, such as mines, tunnel and deep-buried underground powerhouse, rock mass stability is influenced by the excavation and apparent stress concentration at the roof and side wall of such structures. The circular openings are cross-sectional structure in underground engineering, whose progressive fracturing processes have been extensively studied by numerical simulation but lack of experiment researches. In the view of the above factors, uniaxial compression experiments have been carried out in coarse-grained granite samples with a circular opening, together with AE monitoring.
Section snippets
Experimental procedure
Coarse-grained granite that the grain size is from about 2 mm to 9 mm and is about 5 mm in average, were used in this work. The rock was processed to Cubic, with approximately 300 mm in length, 300 mm in height and 100 mm in width. A circular opening of the size ϕ 60 mm was drilled in middle of the specimen, as shown in Fig. 1. A servo-controlled machine with a maximum loading of 3000 kN, which records the amount of load and the degree of displacement in real time, was used during the uniaxial
Determination of the P-wave onset time and the first motion amplitude
Akaike [19] showed that a time series can be divided into locally stationary segments, each modeled as an autoregressive process. The intervals before and after the onset time are assumed to be two different stationary time series. For a fixed order autoregressive process the point at which the Akaike Information Criterion is minimized, determines the separation point of the two time series (noise and signal) and therefore the onset point [20].
For AE waveform, the time series of n data is
Spatial distribution of the micro-cracks
The spatial micro-crack distribution with increasing stress and the picture of macroscopic fractures after the failure of the specimen 502 are shown in Fig. 6. The shear cracks, tensile cracks and mixed-cracks are indicated by red squares, blue circles and green triangles, respectively. For specimen 502, AE sensors were placed at the upper part of the specimen (see Table 1), which is the part where we have focused. Therefore, any AE events that occurred in regions where the AE sensor coverage
Conclusions
In this study, the temporal–spatial evolution of micro-cracks and the behavior of the ratios of three-mode cracks of coarse-grained granite specimens with circular opening under uniaxial compression were studied applying the simplex algorithm and the MT tensor theory, the following conclusions are drawn.
- (1)
The results obtained from the AE hypocenter location and the MT analysis provides information on the spatial distribution and the type of micro-cracks during the experiment. During the loading
Acknowledgements
This work was financially supported by Projects (2013BAB02B01, 2013BAB02B03) of the National Key Technology R&D Program of China, the Projects (51274055, 51204030) of the National Natural Science Foundation of China, and the Projects (N130401006, N120801002, N120701001) of the Fundamental Research Funds for the Central University of China. Project of the Key Science& Technology Special Project of Third Five-Year Plan of MCC (0012012009), Specialized Research Fund for the Doctoral Program of
References (28)
The role of acoustic emission in the study of rock fracture
Int J Rock Mech Min Sci Geomech Abstr
(1993)- et al.
Indicators of critical point behavior prior to rock failure inferred from pre-failure damage
Tectonophysics
(2007) - et al.
Experimental studies of the change of spatial correlation length of acoustic emission events during rock fracture process
Int J Rock Mech Min Sci
(2010) - et al.
Borehole breakout evolution through acoustic emission location analysis
Int J Rock Mech Min Sci
(2010) - et al.
Estimation of cracking and damage mechanisms in rock under triaxial compression by moment tensor analysis of acoustic emission
Int J Rock Mech Min Sci
(2004) - et al.
Comparison of polarity and moment tensor inversion methods for source analysis of acoustic emission data
Int J Rock Mech Min Sci
(2010) - et al.
Robust automatic P-phase picking: an on-line implementation in the analysis of broadband seismogram recordings
Phys Earth Planet In
(1999) - et al.
Simulation of progressive fracturing process around underground excavations under biaxial compression
Tunn Underge Sp Tech
(2005) Magnitude-frequency relation for elastic shocks accompanying fractures of various materials and some related problems in earthquakes
Bull Earthq Res Inst
(1962)The frequency-magnitude relation of microfracturing in rock and its relation to earthquakes
Bull Seismol Soc Am
(1968)
Safety management based on detection of possible rock bursts by AE monitoring during tunnel excavation
Rock Mech Rock Engng
Role of acoustic emission for solving rock engineering problems in Indonesian underground mining
Rock Mech Rock Engng
Excitation of the normal modes of the earth by earthquake sources
Geophys J Roy Astr
Cited by (112)
Mechanical properties and failure behaviour of anchored granite containing two filled edge-notched fissures in triaxial compression
2024, Theoretical and Applied Fracture MechanicsTemperature response of coal fracture induced by three-dimensional stress field
2024, Measurement: Journal of the International Measurement ConfederationFailure behaviors of square-tunnel-structured rock specimens under various inclined boundary stress conditions
2024, Engineering Failure AnalysisFailure mechanism of rock masses with complex geological conditions in a large underground cavern: A case study
2024, Soil Dynamics and Earthquake EngineeringRoadway fracture mechanism investigation subjected to static and blast loading under different lateral pressure coefficients
2023, Engineering Fracture Mechanics