# Laser Vibration Characteristics of Marble Specimens and Failure Criterion
## 1 Introduction  
Laser vibration measurement employing Laser Doppler Vibrometers (LDV) is advantageous in the vibration measurement of structural engineering, as it is optical, remote, non-contacting, and highly sensitive [1, 2]. However, the application of laser vibration measurement in civil engineering is still limited. For example, [PERSON] et al. [3] established a vibration measurement system with LDV and detected the damage on a reinforced concrete deck. [PERSON] and [PERSON] [4] tested the tension level of bridge cable via the non-contacting LDV, and they concluded that the technique was much more effective than the traditional contact measurements. [PERSON] et al. [5] established a practical displacement detection method for a railway bridge through the non-contact ion laser Doppler system. [PERSON] et al. [6] showed the application of in situ measurements of a slab on the building's external wall peeling off and falling to the ground. In geotechnical engineering, new technologies such as LDV are in urgent need for assessing rock stability [7]. Applications of LDV have been commented on in the scientific literature to monitor deformation [8] or to evaluate rockfall hazards [9]. Slope model experiments were conducted to evaluate the influence of discontinuities on rock slopestability. In this type of experiment, a block is put on the slope of a triangular block, and their interfaces are treated as potential slip surfaces. [PERSON] et al. [10] concluded that the LDV could precisely measure the dominant frequency of the block, which was an effective index for evaluating the stability of the rock mass. [PERSON] et al. [11] and [PERSON] et al. [12] further considered the freeze-thawing condition and pointed out that the fundamental natural frequency monitored by LVD could be used to calculate the strength reduction factor and accurately describe the rock stability. Frequency response monitoring is a practical and reasonable method to evaluate the stability of hazardous rock blocks. Acoustic emission (AE) is defined as the transient elastic waveform released by the accumulated localized energy, which is induced by microcrack initiation or expansion [13]. AE technology is now widely used in rock experiments and field monitoring, reflecting the evolution and propagation of cracks [14; 15]. It was concluded that the instantaneously sharp increase of AE parameters (e.g., AE rate, AE counts, and AE energy) are representative of rock failure [16]. For example, [PERSON] et al. [17] divided the AE variation process of rock into a slow growth stage and an accelerated growth stage. [PERSON] et al. [18] found that AE activities were affected by moisture content in rock. The AE counts were stable in the elastic deformation phase, increased rapidly in the plastic phase, and sharply increased in the failure stage. The rapid increase of AE counts represents the rapid development of microcracks, and the sharp increase indicated that the specimens began fracturing. This viewpoint has been verified by many researchers [19; 20; 21]. [PERSON] et al. [22] pointed out that damage occurred at the high-stress level after sufficient energy was accumulated. Based on laboratory results, AE microearthquake monitoring and early warning equipment was developed to forecast coal and gas outburst dynamic disasters [23]. Recently, researchers have turned to focus on waveform-based frequency spectra characteristics. For example, [PERSON] et al. [24; 25] confirmed that the results possessed conformality by using different AE waveform-based algorithms and pointed out that the AE waveform characteristics could be used to analyze the source mechanism. [PERSON] et al. [13; 26] revealed the failure morphology and failure mechanism of shale specimens by distinguishing the high and low AE dominant frequency. [PERSON] et al. [27] conducted Brazilian tests on marble discs and reported that the high AE dominant frequency was caused by shear failure and the low AE dominant frequency was caused by tensile failure. [PERSON] et al.