The specimens were prepared with a cement-based grout for easy casting and eliminating initial heterogeneity of rock material. Specimens prepared using such materials has been widely used to observe the crack behaviour (i.e., Cao et al., 2015; Li et al., 2019) through which the usefulness of such material to model real rock has been demonstrated. The components and proportions of the grout materials are Portland cement, the as-supplied proportions are 30–60%, low quartz fly ash, <9% and additives, >60% respectively. The water to grout ratio was 0.25. A single block was prepared and specimens were cored after 28 days curing time. Three discs prepared for the Brazilian test had a mean diameter of 96.3 mm and thickness of 47 mm. The three specimens used in the uniaxial compression tests had a mean diameter and length of 67.8, 148 mm, respectively. The ends of samples for the uniaxial compression test were ground flat to reduce end effects.

Eight sensors were glued onto each test specimen. Signals are acquired from sensors with preamplifiers to condition the signals prior to being captured by the data acquisition system. The sensors (model Micro 80 and Nano 30) and preamplifiers (model 2/4/6) used in the study were supplied by Physical Acoustics Corporation (PAC). The data acquisition system is based on a National Instruments (NI) high-speed acquisition system acquisition (DAQ) device NI PXIe-6366, which has a maximum acquisition rate of two million samples per second per channel with 16-bit resolution. Signals were amplified at a set gain of 40 dB. In the Brazilian test, four sensors were glued on the front face and another four sensors were on the rear face. The distribution of sensors represented as black dots on the front face is illustrated in Figure 1A. As the events to be located are not completely surrounded, this distribution may not be an optimum design to locate events (Duca et al., 2015). However, this distribution confines ray paths in a smaller volume, i.e. the density of ray paths is larger than sensors completely surrounding the specimen, which improves the accuracy of velocity reconstruction. In the uniaxial compression test, sensors were arranged around the outer surface as indicated in Figure 1B.

Before loading commenced, velocity surveys were performed using pencil-lead break tests as sources on one surface and signals were received by sensors on the opposite surface. The test specimens were then loaded to failure using an MTS model 815 loading system under constant displacement control of 0.003 mm/s. The chosen constant loading rate falls into quasi-static loading condition (Zhang et al., 1999) and ensure enough time for AE recording. The specimen was monitored continuously during the test by an AE data acquisition system (see also Cheng et al., 2013). Signals were sampled at the rate of 2 MHz per channel. When AE signals that were amplified by 40 dB in more than six sensors exceed the threshold that is set to be 100 mV to minimize the recording of noise, it is recognized as an AE count. The events used for tomography are even less as we only selected those with high signal-noise ratios to increase accuracy of velocity redistribution. After the test, the first arrival time was determined using NI Diadem software package that has the capability to visualize and analyze large volumes of data. Signals were also zoomed in and checked manually to ensure the accuracy of first arrivals. The first arrival times were then inputted into a MATLAB code for AE tomography together with the sensor coordinates and an initial uniform velocity model where velocities were set a value of 4 km/s which is the average initial velocity rounded up to the nearest integer. The code undertook a series of iterations until the distance residuals became stable, which was generally within 30 iterations. By multiplying the P-wave velocity model and the associated time residual between each measured travel time and the calculated travel times for that given location, we calculated the distance residual, one of the sources for location errors, to be less than 3 mm in the Brazilian test and less than 10 mm in the uniaxial compression test. This distance residual as shown by Cheng (2014) is much smaller than that calculated by traditional method in which P-wave velocity model is not included. When combined with other sources for location errors, such as arrival time errors and velocity variance in the laboratory test, the source location errors amount to up to 15 mm according to pencil lead break tests. The velocity error tolerance was 22 m/s in both tests with ART tomographic reconstruction convergence value set at 0.0005 and velocity at 4 km/s. Only sources located inside the sensor configuration region were used to perform velocity tomography as the source locations inside the sensor array are considered to be more accurate than those outside (Hardy, 2003) and large source location errors can cause large velocity errors (Schubert, 2004).

The basic concept of AE tomography technique is that AE events are used as point sources for tomographic reconstruction. In contrast to traditional tomography, both source locations and travel times are unknown. AE source location algorithm and tomography image reconstruction algorithm are iteratively combined. A computer algorithm was developed to process large amount of elastic wave data for the purpose of AE source location and tomography reconstruction with the standard procedures shown in Figure 1. More details of the algorithm can be found in the literature (Schubert, 2006; Cheng et al., 2015).

The velocities of elastic waves are affected significantly by the volume, distribution and shape of cracks in the rock (Walsh, 1965a; O’Connell and Budiansky, 1974; Paterson and Wong, 2005). It is known that P wave velocity may decrease substantially in the presence of thin cracks (e.g., Hadley, 1976). In a stressed rock volume, tensile cracks open preferentially parallel to the maximum compressive stress direction (Tapponnier and Brace, 1976; Reches and Lockner, 1994). The velocity propagating in the direction perpendicular to the planes of preferred crack orientation is more significantly reduced than that parallel to the crack planes (Nur, 1971; Bonner, 1974; Lockner et al., 1977; Schubnel et al., 2003). Elastic constants and crack damage can be estimated from elastic wave velocities (Soga et al., 1978; Ayling et al., 1995; Mavko et al., 1998; Schubnel et al., 2003).

We use the model of Soga et al. (1978) to invert crack densities from the velocity data. The classic model by Soga et al. (1978) relates the velocity changes to the evolution of stress-induced micro-cracking and dilatancy. It is so efficient that only limited numbers of input (velocity) are required but useful insight into the micromechanics could still be provided. For example, Stanchits et al. (2006) showed that crack densities in triaxial compression tests on Etna basalt and Aue granite predicted by the approach of Soga et al. (1978) are very similar to the self-consistent model by O'Connell and Budiansky (1974) which also require measurement of the effective bulk modulus and Poisson ratio. Flat spheroidal cracks are assumed oriented perpendicular to three orthogonal directions (Andersson et al., 2009).). Oblique cracks may also exist but the effects on velocity can be considered vectorially divided between those of the three mutually perpendicular crack types. For an isotropic material, the crack density is related to P-wave velocities by the equation: ρ = 1 − ( P P 0 ) 2 a 1 + 2 a 2 (1)

P₀ is the P-wave velocity of the crack-free rock and the coefficients a ₁=1.452 and a ₂=0.192 are given by Soga et al. (1978). Following Stanchits et al. (2006) the unknown P ₀ is taken as 1.05 times the maximum registered P-wave velocity leading to P ₀=4.115 km/s.

With increased load, specimens separated into two halves with the splitting surfaces sub-parallel to the loading axis as shown in Figure 2. The average strength of the test specimen was determined as 2.2 MPa and the axial stress-time curve for one disc is shown in Figure 3. Results presented are always for this disc unless otherwise stated.

The entire failure process can be divided into three stages based on the stress-strain and AE count curves. The relationship between the three stages and axial stress-time is also displayed in Figure 3. AEs recorded after peak load reached were excluded in the curve. The average time interval of the three stages was around 35.3 s. In total, 36, 41 and 39 events with high signal-noise ratios were selected for Stage I, II and III, respectively, to locate AE source locations and perform velocity redistributions. Tomography was performed with specimens discretized into 90 cells with a single cell size of 11 × 8 × 10 mm³. The stress intervals and number of events and rays (i.e. number of sources multiplied by number of receivers) corresponding to the three stages are displayed in Table 1.

Initially there is a slow rise in the number of AEs until it reaches a threshold and the count remains almost constant for 20 s as shown in Figure 3. This corresponds to what is referred to as Stage I behavior. It is thought that during this period pre-existing micro-cracks are prone to be closed under compressive stresses. Stage II is marked by a steady but constant increase of count. In Stage III there is an increasing count of signals with a rapid rise just at the onset of failure. The count rate then reduces after specimen failure. AE count increases almost linear with axis strain before failure. The gradual increase indicates that the failure was formed by progressive clustering of micro-cracks (Falls 1993). To facilitate understanding of each stage, we name each stage following the work of Martin and Chandler (1994), based on the above observations.

The failure modes of the uniaxial compression test specimen were a mix of splitting and shearing. In Figure 8A cracks were observed to split the specimen parallel to the loading direction and in Figure 8B, shearing of the specimen could also be seen along an oblique plane and near the loading end. Notably, shearing occurred near the peak stress and the small piece shown in Figure 8B was not completely detached. It was separated after the test for the purpose of showing details of failure planes. An end cone caused by platen restraint is also visible.

The uniaxial compression strength of the sample was measured as 41.3 MPa and the stress-time curve is shown in Figure 9. The time to failure was approximately 377 s. The stress-time curve is quite typical, with four regions. The first region is with positive curvature illustrated as Stage I. The second region is a nearly linear curve and includes Stage II and III. The third region is with negative curvature shown as Stage IV and the final curve is the post peak region represented as Stage V. The acquired signals were divided into five stages for processing and analyzing AE and tomographic images.

The average time interval of the five stages was around 75.7 s, excluding the post-failure zone. A total of 31, 39, 32, 59, and 28 events with high signal-noise ratios were selected for Stage I, II, III, IV, and V, respectively, to locate AE sources and perform velocity redistributions. Tomography was performed with specimens discretized into 810 cells with a single cell size of 9 × 9 × 10 mm³. The time and stress intervals and number of processed events and rays corresponding to the five stages are displayed in Table 2.

For the uniaxial compression test, initially AE count increases steadily until around 70 s and then remained unchanged as load increased within the elastic range for around 240 s. As load further increases, AE count begins to increase very rapidly while the force-time curve becomes highly non-linear. The count stays low until just before failure and increases when stress rises to about 90% of the peak stress (Figure 9).

We discuss in the following the failure process during the two tests. Despite only one test per each testing scenarios was presented, the statistical reliability of experimental results might be indicated by the uncertainty associated with the test measurements and calculation of AE parameters. Because specimens used in this study are made of rock-like materials which are known for producing relatively homogenous specimens (Cao et al., 2015; Li et al., 2019). As a result, assuming homogeneity of specimens on the spatial scale indicates that measurement uncertainty exceeds the standard deviations of the performed tests.

The located AE hypocenters and velocity diagrams show distinct features for uniaxial compression tests and Brazilian tests. The AE hypocenters in Figure 10 and velocity diagrams in Figure 13 for uniaxial compression tests showing several separated zones where the p-wave velocity increased significantly during loading indicates that the damage is quite diffused and that crack initiates at several locations until they coalescent to form a macroscopic fracture. Similar observations on such a diffused damage zone preceding the occurrence of brittle fracturing have also been reported in rock failure under compressive stresses (i.e., Yang et al., 2021). Different to uniaxial compression tests, the Brazilian tests exhibit a localized damage zone, as revealed in Figure 4 and Figure 6, indicating the location for tensile fracturing, which is consistent with previous analytical studies (i.e., Russell and Muir Wood, 2009) that the failure is controlled by the tensile strength and crack initiates at the largest tensile stress beneath the loading point. These observations lend support to our hypothesis that the AE sources are predominately mixed types of compressional and shear type events in uniaxial compression tests and are predominantly tensile type in Brazilian tests. Also, the observations that the velocity reduced only after failure in the uniaxial compression test, while in the Brazilian test velocity had already begun to reduce before failure occurred might also be explained by the different types of micro-cracks.

The observed progressive clustering of micro-cracks especially in Brazilian tests support the notion of fracture process zone (FPZ) (Labuz et al., 1987). There are investigations suggesting that the size of FPZ might be estimated with the aid of AE locations (i.e., Zhang and Wu, 1999; Zhou and Zhang, 2021). The more diffused damage zone for uniaxial compression test arising from the compressive stresses than that of Brazilian test indicates the estimation of FPZ size might be more appropriate for Brazilian test. We estimated the width of the localized damage band in Brazilian tests using results in Figure 4c at the magnitude of a few millimetres. When this width of the localized damage band is taken as the FPZ size, it is comparable with estimations reported in the literature for sandstone and granite (i.e., Chen and Labuz, 2006; Zhang et al., 2012).

AE technique has potential applications for forecasting catastrophic rupture in brittle rocks (i.e., Meng et al., 2016; Zhang J-Z. and Zhou X-P., 2020). An improved accuracy of locating AE hypocenter is thus desirable. We demonstrate that the P-wave velocity varies during either uniaxial compression test or Brazilian test because of noticeable changes in micro-crack densities during tests. Therefore, in comparison to an isotropic velocity model, a varying 3D-velocity model as used here is expected to improve the accuracy and reliability of the velocity tomographic images showing the progressive cracking without interrupting the loading process.

In the velocity tomography study, high velocity areas are observed to agree with the highly stressed regions, which is as indicated in theoretical analysis (e.g., Li and Wong, 2013). High velocity areas were also found to occur before the final failure of the specimen which may be used as a precursor of specimen failure.