Tensile strength and failure behavior of rock-mortar interfaces:Direct and indirect measurements

Ghsem Shms ,Ptrice Rivrd ,Omid Mordin

a Civil Engineering and Building Engineering Department,Université de Sherbrooke,Sherbrooke,Québec,Canada

b Department of Earth Sciences,Swiss Federal Institute of Technology (ETH),Zurich,Switzerland

c Department of Civil and Environmental Engineering,Colorado School of Mines,Golden,CO,USA

Keywords: Rock-mortar Rock-concrete Moment tensor inversion (MTI)Acoustic emission (AE)Digital image correlation (DIC)Tensile strength Direct tensile test Brazilian test

ABSTRACT The tensile strength at the rock-concrete interface is one of the crucial factors controlling the failure mechanisms of structures,such as concrete gravity dams.Despite the critical importance of the failure mechanism and tensile strength of rock-concrete interfaces,understanding of these factors remains very limited.This study investigated the tensile strength and fracturing processes at rock-mortar interfaces subjected to direct and indirect tensile loadings.Digital image correlation (DIC) and acoustic emission(AE) techniques were used to monitor the failure mechanisms of specimens subjected to direct tension and indirect loading (Brazilian tests).The results indicated that the direct tensile strength of the rockmortar specimens was lower than their indirect tensile strength,with a direct/indirect tensile strength ratio of 65%.DIC strain field data and moment tensor inversions (MTI) of AE events indicated that a significant number of shear microcracks occurred in the specimens subjected to the Brazilian test.The presence of these shear microcracks,which require more energy to break,resulted in a higher tensile strength during the Brazilian tests.In contrast,microcracks were predominantly tensile in specimens subjected to direct tension,leading to a lower tensile strength.Spatiotemporal monitoring of the cracking processes in the rock-mortar interfaces revealed that they show AE precursors before failure under the Brazilian test,whereas they show a minimal number of AE events before failure under direct tension.Due to different microcracking mechanisms,specimens tested under Brazilian tests showed lower roughness with flatter fracture surfaces than those tested under direct tension with jagged and rough fracture surfaces.The results of this study shed light on better understanding the micromechanics of damage in the rock-concrete interfaces for a safer design of engineering structures.

1.Introduction

In geomechanics,rock-concrete interfaces are frequently seen in civil and mining engineering applications such as concrete gravity dams founded on rock,concrete retaining walls,socketed piers,and shotcrete (Fishman,2009;Chang et al.,2018).In such structures,the interface between rock and concrete is usually considered the weakest structural zone,causing the initiation and growth of damage and final failure along the interface (Zhong et al.,2014;Dong et al.,2019).During the last few decades,numerous studies have investigated the mechanical behavior of rock-concrete interfaces under compression(Saiang et al.,2005;Sel?uk and As?ma,2019) and shear loading (Kodikara and Johnston,1994;Moradian et al.,2010;Tian et al.,2014;Andjelkovic et al.,2015;Mouzannar et al.,2017;Gutiérrez-Ch et al.,2018).However,very few studies have focused on the tensile interaction mechanism and tensile strength of rock-concrete interfaces.In brittle materials,tensile strength is often less than shear strength and much smaller than compressive strength,reflecting the importance of tensile strength in the resistance to failure of rock engineering materials and rockconcrete structures (Griffith,1924;Perras and Diederichs,2014;You,2015).For instance,the tensile strength in dam-foundation interfaces resists the overturning moment at the toe zones of dams due to the acting forces of reservoirs(Electric Power Research Institute(EPRI),1992;Jawalkar,1996).In addition,tensile failure at the rock-shotcrete interface is the source of instabilities and the failure mode in shotcrete,which,in turn,can influence the overall stability of structures (Barrett and McCreath,1995;Son,2013;Chang et al.,2018;Zhu et al.,2020).Furthermore,the tensile strength and behavior at cement-cap rock interfaces are crucial factors controlling leakage from wells in the oil and gas industry(Tors?ter et al.,2015;Stroisz et al.,2019).Therefore,to provide a safe design of elements incorporating rock-concrete interfaces,obtaining a reliable understanding of the tensile behavior of such bi-material interfaces and its impact on the fracturing processes of whole structures is essential.

It should be noted that there is no standard laboratory testing procedure for performing a tensile test on a rock-concrete or rockmortar interface,with direct tension and Brazilian (indirect) tension tests typically being adopted(Electric Power Research Institute(EPRI),1992;Mouzannar et al.,2017;Chang et al.,2018).Based on the existing literature,the failure properties and Brazilian tensile strength (BTS) of rock-concrete and rock-mortar specimens subjected to the Brazilian test are controlled by various parameters,including the interface roughness,interface inclination angle,rock type,and concrete/mortar properties (Chang et al.,2018;Sel?uk and As?ma,2019;Qiu et al.,2020;Zhou et al.,2020;Zhu et al.,2020).

Some studies have reported that the BTS of rock-mortar specimens increases with interface roughness (Luo et al.,2017;Chang et al.,2018;Qiu et al.,2020;Zhu et al.,2020).According to previous studies (Qiu et al.,2020;Zhu et al.,2020;Shams et al.,2022),increasing the interface roughness increases the contact area and interlocking effect(anchorage)between the rock and mortar along the interface.This contributes to an increase in the BTS of rockmortar Brazilian discs.Luo et al.(2017) observed that the BTS of rock-mortar interfaces is governed by the combined contribution of the adhesion and cohesion losses.Adhesion loss occurs when rock and concrete/mortar semi-samples are detached exactly along their interface,without any failure in the interface asperities.In cohesion loss,failure occurs at the asperities root,either in the concrete/mortar or rock.

The BTS of rock-mortar interfaces is also affected by the properties of the rock and mortar constituents.Chang et al.(2018),Sel?uk and As?ma (2019),and Zhu et al.(2020) showed that an increase in the mortar strength increases the BTS of bi-material discs.According to studies of Sel?uk and As?ma (2019) and Zhu et al.(2020),the mortar constituents and degree of hydration of the cement produce different adhesions between the rock and mortar that affect the BTS of specimens.Moreover,the mechanical properties of rocks seem to have a negligible effect on the BTS of bi-material specimens as long as the mortar is weaker than the rock (Qiu et al.,2020;Zhu et al.,2020).It has also been shown that the interface adhesive strength is affected by the physical properties of rocks,for example,porosity(Zhu et al.,2020).For instance,compared with granite and marble,sandstone adheres much more to mortar,thereby increasing the adhesion between rock and mortar and increasing the BTS of rockmortar specimens(Zhu et al.,2020).

The tensile strength of rock-mortar specimens under direct tension has rarely been studied.Bauret and Rivard (2018) studied the effect of interface roughness on the direct tensile strength(DTS)of bi-material cylindrical specimens composed of high-strength and low-strength mortars.Their results indicated that the bond strength increased with roughness.A few studies have reported the DTS of rock-mortar and rock-concrete specimens without examining the effect of different parameters on the DTS(Electric Power Research Institute (EPRI),1992;Saiang et al.,2005;Son,2013;Flansbjer and Magnusson,2014;Mouzannar et al.,2017).Notably,rock-mortar and rock-concrete interfaces have a smaller,yet considerable DTS compared to those of intact rock and intact mortar/concrete (Electric Power Research Institute (EPRI),1992;Mouzannar et al.,2017)and,sometimes,DTS is comparable to that of intact mortar/concrete (Flansbjer and Magnusson,2014).

It is well known that the Brazilian test overestimates the tensile strength of "intact" rocks.The ratio of the DTS to BTS for different"intact"rock types ranges between 0.6 and 0.9(Mellor and Hawkes,1971;Martin and Chandler,1994;Fuenkajorn and Klanphumeesri,2011;Liu et al.,2014;Perras and Diederichs,2014;Cacciari and Futai,2018;Qi et al.,2019;Efe et al.,2021).This difference between the DTS and BTS is mainly attributed to the different loading configurations of the two testing methods (Li and Wong,2013;Perras and Diederichs,2014).According to study results of Perras and Diederichs (2014),a key factor affecting the difference between the BTS and DTS of rocks is suppressed crack propagation in Brazilian discs because of the biaxial stress state in the Brazilian test.However,these very few studies have focused on the macroscale behavior of rocks under tensile loading.Based on a numerical study,Qi et al.(2019)reported that the difference between the BTS and DTS of intact rocks arise because the applied external load must overcome both the tensile and shear strengths along the grain boundaries in the Brazilian test compared to only tensile strength along the grain boundaries in the direct tensile test.In an experimental study,Wang et al.(2019)analyzed the dominant frequency of acoustic emission(AE)hits produced in marble specimens under direct and Brazilian tensile tests.These authors suggested that tensile cracks produce low-dominant-frequency AE signals while shear cracks release high-dominant-frequency signals and concluded that the difference in DTS and BTS of marble results from a higher proportion of high-dominant-frequency waveforms (i.e.shear cracks) in Brazilian test specimens.

While the tensile fracturing processes of "intact" rocks under the Brazilian and direct tensile tests have been investigated to some extent,there are still critical scientific gaps in understanding the micromechanics of the tensile fracturing in bi-material interfaces such as rock-mortar or rock-concrete.Further research is needed to investigate: (1) When,where,and how microcracks nucleate and propagate in these interfaces under tensile loading;(2) Do bimaterial interfaces show precursors before final failure? (3) Do spatiotemporal evolutions of cracking processes in bi-materials differ in micro-and macro-scales? Answering these questions can significantly increase our knowledge for successful health monitoring of engineering structures.

This study investigated the fracturing processes in rock-mortar specimens at the microscopic scale by focusing on spatiotemporal crack initiation and propagation under direct and indirect (Brazilian)tensile tests.In addition,microcrack source mechanisms were examined during the tensile loading of rock-mortar interfaces to better understand the relationship between micro-and macrocracking mechanisms and between the direct and indirect tensile strengths.A combination of strain measurements using digital image correlation (DIC) and moment tensor analysis of AE were used to track the microscopic cracking and damage mechanisms.The roughness values of the fractures produced under the two loading conditions were also compared.Our results provide insight into the fundamental mechanisms of rock-concrete interface fracturing under tensile loading.

2.Specimens,and experimental procedure

2.1.Specimen preparation

The bi-material specimens were composed of rock and mortar.Two groups of rock-mortar specimens were prepared as follows:(1) cylindrical disc specimens,which were subjected to Brazilian indirect tensile loading (B specimens),and (2) rectangular prismatic specimens,which were subjected to direct tensile loading(D specimens).The rock was Stanstead granite,and the mortar was composed of water and SikaGrout 212 in a ratio of 2:11.

A granite panel with a saw-cut smooth surface was used to prepare the rock-mortar specimens.After preparing the granite panel,it was placed in a wooden mold and mortar was poured onto the rock surface in the mold.A plastic sheet was used to cover the cast mortar for 48 h,and once the mortar hardened,the rock-mortar blocks were kept in a wet room at room temperature for 28 d.

Cylindrical cores (diameter,D=75 mm) were subsequently drilled from the rock-mortar blocks,and the drilling axis was parallel to the rock-mortar interface.Careful attention was paid to ensure that the interface passed through the center of the cores.Subsequently,the cores were cut into cylindrical discs(D=75 mm,thickness(T)=37.5 mm)as specimens for Brazilian indirect tensile testing (Fig.1a) with aT/Dratio of 0.5,as suggested by the International Society for Rock Mechanics and Rock Engineering (ISRM)(Bieniawski and Hawkes,1978).Both sides of the discs were then ground and polished.Furthermore,the rock-mortar block was cut into small cuboid samples (length (L) × width (W) × height(H)=37 mm ×30 mm×100 mm)as specimens for direct tensile testing(Fig.1b).The ends of the prismatic specimens were polished and then glued onto the loading plates using a strong adhesive epoxy(Fig.1b).The entire preparation procedure,including coring,cutting,grinding,and polishing,was performed according to ISRM recommendations (Bieniawski and Hawkes,1978;ISRM,2016).

Fig.1.Specimen dimension,location of AE sensors,and speckle pattern created over the front faces of specimens for the (a) Brazilian and (b) Direct tension tests.

High-contrast black speckles were made on a white layer of paint on the surfaces of the specimens to achieve more accurate displacement measurements using DIC technique,as depicted in Fig.1a and b.In addition,cylindrical and disc specimens of intact mortar and granite were prepared to determine basic mechanical and physical properties,as listed in Table 1.

Table 1Mechanical and physical properties of Stanstead granite and mortar.

Uniaxial compression tests were conducted on the cylindrical specimens of granite and mortar (D=54 mm,H=110 mm,H/D=2).The specimens were loaded axially until failure using a material testing system (MTS).Axial load,axial displacement,and transverse displacement were recorded during the experiments.Two linear variable differential transformers (LVDT) were used to record the axial displacement along the loading direction.A circumferential extensometer with a roller chain was used to measure the lateral deformation at the mid-height of each specimen.The unconfined compressive strength (UCS) of each specimen was then calculated by dividing the peak load by the crosssectional area.The tangent Young’s modulus was then determined from the linear part of the axial stress-strain curves.Poisson’s ratio was also measured as the ratio of the lateral strain to the axial strain at the failure load.

Brazilian tensile tests were also performed on cylindrical disc specimens of intact granite and intact mortar,and direct tensile tests were conducted on rectangular prismatic specimens of intact granite and mortar.The testing procedures for both tests were the same as for the granite-mortar specimens (see Section 2.2).

Finally,Pundit ultrasonic velocity testing equipment was employed to measure P-wave velocity (Vp).The pundit system comprises a pulse transmission generator,transducers,and an electronic tester for time-interval measurements.Vpwas calculated from the measured travel time and distance between the transmitter and receiver on the cylindrical granite and mortar specimens.

2.2.Experimental system and testing method

2.2.1.Loading system

Brazilian tests were performed using a servo-controlled MTS.The load cell capacity for the Brazilian tests was 225 KN.Direct tensile tests were performed with an INSTRON 4482 dual-column Universal Testing machine,for which the load cell capacity was 100 KN.

ISRM standard loading jaws (Bieniawski and Hawkes,1978)were used to perform the experimental Brazilian tests (Fig.1a).In addition,two cardboard cushions (T=2.5 mm) were inserted between the jaws and specimens (Fig.1a) to avoid an excessive concentration of compressive stress at the jaw-specimen contact(Mellor and Hawkes,1971;Perras and Diederichs,2014;García et al.,2017),which would otherwise cause premature fracture initiation and invalidate the test results(Mellor and Hawkes,1971;Yuan and Shen,2017;Lu et al.,2018).

All the tests were performed at the Rock Mechanics Laboratory of the Université de Sherbrooke,located in Sherbrooke,Quebec,Canada.Two LVDT displacement transducers(Solartron Metrology,Model 925,604 DCR15)were used to record the axial displacement in the vertical direction in both direct and Brazilian tests.To ensure that the experiments were performed under a quasi-static loading condition,they were conducted in the displacement control mode at a rate of 0.1 μm/s.The average test durations for the Brazilian and direct tensile tests were 196 min and 42 min,respectively.This loading rate,which was lower than the ISRM recommendation(Bieniawski and Hawkes,1978),was adopted to better monitor and record the fracturing processes in the specimens.

2.2.2.Acoustic emission (AE) monitoring

MISTRAS μ-SAMOS AE equipment with two PCI-8 cards (16 measurement channels) was employed to detect the spatiotemporal evolution of AE events (microcracking) in the specimens throughout the experiments.Nano-30 AE sensors operating in the 125-750 kHz frequency range,with a resonant frequency of 300 kHz,were employed to record AE signals.Fig.1a and b shows the AE sensor arrangement for the Brazilian and prismatic specimens,for which ten and eight AE sensors were attached,respectively.To obtain the three dimensional (3D) spatial distribution of the AE events: (1) for the Brazilian specimens,four sensors were mounted on the front surface,four on the back surface,and two on the sides (Fig.1a);and (2) for the specimens under direct tensile loading,four sensors were placed on the back surface and four on the left and right sides(Fig.1b).The sides of the discs were slightly flattened to provide better coupling between the sensors and the specimens.The sensors were first attached to the surfaces of the specimens using double-sided adhesive tape(DSAT)and then glued to the specimens with hot glue.The efficiency of the sensorspecimen coupling was verified using an auto-sensor test (AST)(Grosse and Ochtsu,2008).

PAC 2/3/4 preamplifiers with a gain of 40 dB were employed to amplify the low-amplitude AE signal produced by the AE sensors.To avoid ambient noise as much as possible,AE signals were recorded using a threshold value of 35 dB.The sampling frequency was 3 MHz with a pre-trigger of 50 μs and a sample length of 4096.To compute the AE features,the Peak Definition Time (PDT),Hit Definition Time(HDT),and Hit Lockout Time(HLT)were set as 200 μs,800 μs,and 350 μs,respectively.The maximum duration was 10 ms.The same settings were used for both the Brazilian and direct tensile tests.

AE source localization was performed by determining the arrival times of the P-waves using the Akaike information criterion (AIC)(Kurz et al.,2005;Ohno and Ohtsu,2010).A constant P-wave velocity field model,optimized using the downhill simplex optimization method (Nelder and Mead,1965),was applied to locate the AE sources for a minimum distance error of 3 mm.We followed the procedure developed by Li et al.(2019) for the source localization and moment tensor inversion(MTI)of AE events.It should be noted that the source localization procedure requires that each event triggers a minimum of four observation points (AE sensors) to determine the four unknowns,including the event origin coordinates (x,y,z) and event time (t).Therefore,we applied the minimum four-sensor criterion to locate the AE events.In addition,the AE source mechanism was analyzed using the MTI method to gain insights into microscale cracking during the loading process(Li et al.,2019).Source localization was performed for a minimum of six AE sensors when the AE source mechanisms were investigated using MTI.

A sensitivity analysis was conducted to determine the effect of the P-wave velocity on the location and number of captured AE events.The results indicated a negligible error in the location and number of detected AE events for the range of P-wave velocities from 4.12 Km/s (average for granite,see Table 1) to 4.17 Km/s(average for mortar).Thus,a constant P-wave velocity of 4.15 Km/s was employed to monitor the AE events in the tested rock-mortar specimens.

2.2.3.Imaging system and DIC technique

The DIC technique determines the displacement and strain fields by comparing images of the specimen surface captured at different loading times.First,an image of the specimen surface was taken before loading,called the reference image.A region of interest(ROI)was then defined on the surface of the reference image,over which the deformation was determined.The ROI was composed of smaller regions called subsets.The correlation algorithm identifies the best match between a given subset in an undeformed image (i.e.,the reference image) and a distorted image(i.e.,taken at different loading stages).Finally,the displacement and strain fields were determined by calculating the motion of the subsets (Sutton et al.,2009).

A Basler acA2440-75μm camera with a Scheinder Xenoplan 1.9/35-0901 CM120 BK 15 compact lens was employed to capture images of the specimen during the entire loading process.Images were acquired at a rate of 1 fps with a resolution of 2448 × 2048 pixels.The same imaging rate was employed for both types of tests.To minimize out-of-plane motion and thereby increase the accuracy of the in-plane displacement measurements,the camera was placed 90 cm from the front surface of each specimen.Simultaneously,the lens axis was perpendicular to the specimen surface.Given the small dimensions of the specimens,this distance ensured that the out-of-plane displacement did not exceed the acceptable range (Sutton et al.,2008).Two light emitting diode (LED) lights also cast stable,constant illumination over the surfaces of the specimens,thereby minimizing DIC post-processing errors.

To increase the accuracy of the DIC post-processing,a random speckle pattern was applied over the front surface of the specimens(Sutton et al.,2009).The surfaces of the specimens were lightly coated with white paint,and black paint was sprayed over the surface(Fig.1a and b).Further details on the DIC technique and the speckle patterns are provided by CorelatedSolutions (2020).After capturing the images,the VIC-two dimensional (2D) DIC measurement system(CorelatedSolutions,2020) was used to compute and visualize the displacement and strain fields over the surfaces of the granite specimens.

Following image acquisition,the spatiotemporal evolution of strain fields over the specimen surfaces was computed using VIC-2D software (CorelatedSolutions,2020).The ROI for the specimens tested under the Brazilian and direct tensile loadings were selected such that they covered the area where the final macroscopic fractures occurred(see Figs.4 and 6).A subset size of 29×29 pixels was selected to ensure a unique speckle pattern within each subset(Sutton et al.,2009;CorelatedSolutions,2020).In addition,a step size of seven pixels was selected between the subset meshes to obtain independent and non-repetitive data points over the specimen surfaces (Sutton et al.,2009;CorelatedSolutions,2020).Before each experiment,all observational systems,including the loading,AE monitoring,and imaging systems,were triggered simultaneously to acquire synchronized experimental data.

3.Experimental results

3.1.Tensile strength

Fig.2 shows the load-axial displacement curves of the specimens subjected to Brazilian (six B specimens) and direct tensile(four D specimens)loadings(insets show the corresponding tensile strengths of the specimens).The direct and indirect tensile strengths of the specimens were determined in compliance with ISRM standards (Bieniawski and Hawkes,1978),as given in the Appendix.As the ISRM suggested equation for determining the BTS(i.e.Eq.(A2))is valid for isotropic brittle materials(Bieniawski and Hawkes,1978;Claesson and Bohloli,2002),this was used to calculate the nominal BTS of the rock-mortar specimens for comparison.The nominal tensile strengths(σB)of B1 to B6 ranged from 3 MPa to 3.4 MPa with an average of 3.2 MPa(Fig.2a),and those of D1 to D4 (σD) ranged from 2 MPa to 2.2 MPa with an average of 2.1 MPa(Fig.2b).Thus,on average,the tensile strength of the rockmortar specimens obtained under direct tension was lower than that under indirect(Brazilian)tension,and the ratio of the average direct to Brazilian tensile strength of the rock-mortar specimens(σD/σB) was 0.66.For comparison,reported equivalent ratios for intact rock materials range between 0.6 and 0.9 (Liu et al.,2014;Perras and Diederichs,2014;Cacciari and Futai,2018;Qi et al.,2019;Efe et al.,2021).Thus,the tensile strength ratio of the rock-mortar specimens fell within the range of intact rock materials.

Fig.2.Load-axial displacement of (a) B and (b) D specimens.The insets show the tensile strength values.

3.2.Acoustic and visual observations of fracturing processes

Fig.3 shows the applied load,instantaneous AE hits,and cumulative AE hits versus loading time(represented as a percentage)for two Brazilian specimens:B1 and B2.The scatter plot represents instantaneous AE hits colored by amplitude.To obtain a more representative deformation response of the entire specimen,the AE hits captured by all AE sensors are plotted in Figs.3 and 5.

Fig.3.Instantaneous hits,cumulative hits,and load against the normalized time (t/tmax) × 100 for (a) B1 and (b) B2.

AE hits reflect the internal damage of the loaded specimens,and an increasing hit rate reflects more severe damage (Grosse and Ochtsu,2008;Moradian et al.,2016).Hence,the lack of AE hits for loads lower than 1 KN(indicated by yellow arrows in Fig.3a and b)indicates that no microcracks occurred in B1 or B2 during the initial loading phase.For loads higher than 1 KN,microcracks appeared in both B1 and B2,and progressively accumulated until failure.The constantly increasing trend in the cumulative hit curves in Fig.3a and b reveals that the fracturing processes of both B1 and B2 occurred at a continuous progressive rate.Because the trends of the instantaneous and cumulative hit curves(i.e.,fracturing processes)were similar between B1 and B2 (Fig.3a and b),for the sake of brevity,only the fracturing process of B1 is further discussed.

Fig.4a-e illustrates the AE and DIC results for B1 at five different loading levels,including 25%,50%,75%,95%,and 100% of the failure load(Fp);points P1-P5 are shown by red arrows on the load-time curve(Fig.3a).The major principal strain (extensile strain,ε1) distribution was investigated at points P1-P5.Considering the loading configuration in the direct and Brazilian tests,the major principal strain concentration occurred in the horizontal direction owing to the induced horizontal tensile stress.By contrast,in the direct tension test,the major principal strain was concentrated in the vertical direction.Moreover,because shear damage in brittle materials occurs along the plane of maximum shear strain γmax(Shirole et al.,2020;Zafar et al.,2022),the maximum shear strain distribution was also examined to study the shear micro-damage in the specimens.γmaxwas computed by(Shirole et al.,2020):

Fig.4.(a)-(e) AE and DIC results for B1 corresponding to points P1 to P5 (as shown in Fig.3a).Upper panel: Full-field major principal strain (ε1) obtained by DIC.Lower panel:Spatial distribution of AEs.The blue line represents the observed macroscopic fracture path,and(f)Specimen failure pattern and interfacial failure morphology with projected AE events.Black lines indicate the mortar remaining on the surface of the granite.

where ε2is the minor principal strain.

In Fig.4a-e,the upper panel (UP) depicts the spatiotemporal evolution of the major principal strain(ε1)fields,the middle panel(MP) represents the spatiotemporal evolution of the maximum shear strain (γmax) fields,and the lower panel (LP) shows the spatiotemporal development of AE events.Here,the AE signals captured by at least four AE sensors were considered events.In total,94 AE events were observed during the deformation of B1,as shown in Fig.4e,in which the colors of the AE events (circles)reflect the microcrack occurrence time.The positive strains are referred to as tensile in the strain plots,whereas the negative strains are compressive.Thus,ε1was predominantly tensile in the entire ROI,whereas some compressive strain zones developed around the loading jaws because of the compressive stress field in the vicinity of the jaw-specimen contact area (Hondros,1959;Fairhurst,1964).

Similar to the hit plot in Fig.3a,the spatial distribution of AE events at points P1-P5 in the LP in Fig.4a-e indicates a continuous evolution of microcracks in B1 from small loading values up to the failure load.As shown in Fig.4a,approximately 3% of the total detected AE events (3 AEs) occurred up to P1 (25% Fp).Furthermore,Fig.4a indicates a small heterogeneity in the ε1strain field,whereas the γmaxstrain field remained entirely homogenous.That is,at 25% Fp,the ε1strain plot shows zones of small tensile strain accumulation in B1,whereas there is no visible shear strain accumulation within the specimen.Note that the tensile strain values in the mortar were greater than those in the granite,which is attributed to the heterogeneity of the mechanical properties of the rock-mortar specimens and the difference in Young’s modulus of 29 GPa for mortar versus 50.6 GPa for granite(Table 1).At 50% and 75% of the peak load (marked as points P2 and P3 in Fig.3a),B2 registered 10 and 17 AE events,constituting 11% and 18% of the total events captured (Fig.4b and c).The locations of the AE events reveal progressive damage in the mortar with a few random microcracks in the granite.The ε1strain fields at points P2 and P3(Fig.4b and c)display higher values of tensile strain accumulation in the mortar,which is consistent with the development of the AE events.At 75% Fp,a tensile stress concentration zone began to appear along the interface at the center of B1 (blue rectangle in Fig.4c);however,the tensile strain values in the mortar were still greater than the tensile strain along the interface.The shear strain plots at P2 and P3(Fig.4b and c)suggest that the heterogeneity of the γmaxstrain field remained minimal,meaning no significant shear zone concentration formed in B2 up to 75% Fp.At 95% Fp,approximately 38% of the total AE events were captured,most of which were in the mortar (Fig.4d).In addition,while the tensile strain in the mortar was still more significant than in the granite,the highest tensile strain values appeared to be concentrated along the interface rather than in the mortar (Fig.4d).In addition,the γmaxstrain field at 95% Fp revealed that some shear strain started to occur and accumulated along the interface at this load level(shown by the red rectangle in Fig.4d).This increase in the heterogeneity of the γmaxstrain fields at high loading levels (at ＞75% of the peak load) has been previously reported (Diederichs,2003;Gao et al.,2016;Shirole et al.,2020).Finally,58 new AE events (62% of the total)were captured at 95%-100% Fp(P4 to P5 in Fig.3a),indicating that considerable damage within B1 occurred during a short loading period.Interestingly,in Fig.4e,the 58 newly detected AE events(red circles)were predominantly located either at the exact interface(or in the mortar but very close to the interface)where the highest tensile(ε1)and shear(γmax)strain concentrations were also observed (Fig.4e).Specimen B1 eventually failed along the interface despite the previous internal microcracking in the mortar(Fig.4f).

Fig.4f shows the specimen failure pattern and interfacial failure morphology of specimen B1,in which the spatial distribution of the AE events captured up to the failure time is projected over the interface surface.Some mortar remained on the granite surface along the interface (black lines).That is,B1 failed in both the adhesive (detachment along the interface) and cohesive (internal damage in mortar) loss modes.This suggests that the internal micro-damage in the mortar,which began at lower load levels and accumulated under the gradually increasing load,significantly affected the strain distribution along the interface.Therefore,at higher load levels,the strain concentration rate along the interface exceeded that within the mortar(Fig.4d and e).Thus,the combined damage to the mortar and interface led to strength degradation and final failure along the interface.

Fig.5a and b shows the instantaneous and cumulative hits and the applied load against the loading time (as a percentage) for D1 and D2.The low number of low-amplitude instantaneous hits and the slow growth of cumulative hits indicate that no significant microcracking occurred in these samples until the peak load was reached.Indeed,for both D1 and D2,the cumulative hit number increased dramatically (with high-amplitude hits) at approximately the peak load,leading to ultimate failure,which is indicative of brittle failure.

Given the similar trends in AE hits and microcracking processes between D1 and D2,we will focus on analyzing the evolution of DIC strain and AE events specifically in D1.Thus,the progression of the ε1and γmaxstrain fields and AEs for DI were evaluated at four different loading levels,i.e 50%,75%,95%,and 100% of the failure load(Fp),and points P1-P4 are indicated by red arrows in Fig.5a.

The AE distributions in Fig.6a-c indicate that no microcracking occurred in D1 for load levels below 95% Fp.This was confirmed by the ε1and γmaxstrain fields.The shear strain values were minimal,almost up to P3 (95% Fp),and the γmaxstrain field remained homogenous with little/no visible shear strain concentration.Moreover,the ε1strain field remained homogenous until 75% Fp,whereas some tensile strain concentration zones started forming along the interface at load values of approximately 95% Fp.In addition,like B1,the tensile strain values were more significant in the mortar than in granite.As the applied load approached its maximum value,nine new microcracks(almost 82% of the total AE events) occurred inside D1 within a short period (red circles in Fig.6d);the coalescence and propagation of these microcracks led to the brittle failure of D1.These AE events mainly accumulated on the right side of the specimen,primarily inside the mortar and around the interface.The ε1and γmaxstrain fields both showed their highest strain accumulations at the right side of the specimen and along the final macroscopic fracture.The locations of the highest strain concentration zones strongly matched the AE locations at failure(Fig.6d).It should be noted that(i)the tensile strain values in the mortar exceeded those in the granite during the entire loading process,and (ii) the maximum values of ε1and γmaxat failure were approximately 980 με and 300 με,respectively.The point at which the shear strain was far smaller than the tensile strain at failure may indicate the minor role of shear microcracking in the entire failure process of D1.

Fig.6e depicts the failure pattern of D1 and its interfacial failure morphology.Some mortar remains on the granite surface (as shown by the black lines),while no damage was observed in the granite.AE events are also projected onto the interface in Fig.6e.Notably,the location of the AE events is consistent with the location of the damage in the mortar.In addition,the interfacial failure morphology reveals that macroscopic failure occurred via a combination of adhesive loss(rock-mortar detachment at the interface)and cohesive loss(damage in the mortar).In other words,it appears that the tensile strength of D1 was governed by both the interface and mortar properties.

3.3.AE microcracking source mechanisms

To further investigate the damage mechanisms in the specimens subjected to direct and Brazilian tensile tests,the cracking mechanisms in B1 and D1 were determined by MTI analysis of the AE events according to the 2D implementation of the simplified Green’s function for the moment tensor analysis(SiGMA)(Li et al.,2019).Moment tensors were decomposed into double-couple(DC),isotropic (ISO),and compensated linear vector dipole (CLDV)components for each event,according to Vavry?uk (2015).AE events were subsequently classified as tensile (ISO ≥15% and CLVD ≥-15%),compaction(ISO ≤-15% and CLVD ≤15%),or shear(|ISO| ＜15%) events (Davidsen et al.,2021).

In the MTI analysis,only AE events with a minimum of six Pwave arrival detections were selected for further analysis.Accordingly,37 and seven AE events (with at least six P-wave arrivals)were obtained for B1 and D1,respectively,as shown by the colored circles in Fig.7a and 8a.The size and color of the AE events(circles)reflect their average focal amplitude (A0),calculated considering geometrical spreading for a reference distance of 10 mm,following Zang et al.(1998):

Fig.7.Spatial distribution of AE events up to failure and AE focal mechanisms for B1: (a) AE events with at least six P-wave arrivals,37 AEs that is equal to 100% of AE events captured by at least 6 AE sensors,(b)tensile microcracks,10 AEs that is equal to 27% of all AE events captured(c)compaction microcracks,12 AEs that is equal to 32% of AE events captured,and(d)shear microcracks,15 AEs that is equal to 41% of AE events captured.The color bar corresponds to the average focal amplitude(A0)of AE events(Eq.(2)),where the amplitude is measured in volts.

wherenis the number of sensors receiving the same AE signal,Aiis the amplitude (V) of the first motion signal received by theith sensor,andri(in mm)is the signal source distance to theith sensor.

In Figs.7 and 8,the blue lines indicate the observed ultimate macroscopic failure paths,and the black squares represent the AE events with at least four P-wave arrivals,as shown in Figs.4 and 6.

The spatial distribution of different AE source mechanisms at the failure time is illustrated in Fig.7b-d for B1 and Fig.8b-d for D1.The number and percentage of each AE mechanism are shown below the corresponding subplots,and the blue lines indicate the final macro-fracture path.It should be noted that the orientations of the tensile AE events in Fig.7b and 8b represent the orientations of the tensile microcracks.Further details on determining the orientation of AE events can be found in Grosse and Ochtsu(2008).The orientation of the tensile AE events followed the direction of the ultimate macro-fractures in both specimens,which were vertical to sub-vertical in B1 and horizontal to sub-horizontal in D1.

Fig.8.Spatial distribution of AE events up to failure and AE focal mechanisms for specimen D1: (a) AE events with at least six P-wave arrivals,7 AEs that is equal to 100% of AE events captured by at least 6 AE sensors,(b)Tensile microcracks,6 AEs that is equal to 86% of all AE events captured,(c) Compaction microcracks,1 AEs that is equal to 14% of AE events captured,and (d) Shear microcracks,no shear AE event was detected.The color bar corresponds to the average focal amplitude (A0) of AE events (Eq.(2)),where the amplitude is measured in volts.

As shown in Fig.7,the microcracks of B1 consisted of 27% tensile(10 AE events),32% compaction (12 AE events),and 41% shear (15 AE events) microcracks.Thus,the fracturing processes and tensile strength of B1 were governed by the different contributions of all three microcrack types.In addition,the locations of the tensile and shear microcracks in Fig.7 were consistent with the locations of the tensile and shear strain concentration zones in Fig.4.

For D1,the microcracks were composed of 86% tensile (6 AE events),14% compaction (1 AE event),and 0% shear (0 AE events)cracks (Fig.8).This strongly agrees with the corresponding ε1and γmaxstrain fields at failure for this sample(Fig.6d).Compared with the ε1strains in Fig.6d,the magnitude of the γmaxstrains remained very small,even at the failure time.This shows that D1 failed under a predominantly tensile mode,whereas shear microcracking had a minimal effect on the overall fracturing process,which tallies with the MTI results shown in Fig.8.

From a macroscopic point of view,it is accepted that rock specimens fail under a tensile failure mode under both Brazilian and direct tensile loadings (Bieniawski and Hawkes,1978;Perras and Diederichs,2014;ASTM D3967-16,2016).However,the DIC strain fields(Figs.4 and 6)and AE focal mechanisms(Figs.7 and 8)indicate that the so-called macroscopic tensile failure of the rockmortar specimens consisted of tensile,compaction,and shear cracks at the microscale,while the relative proportions of these cracking modes varied between the loading configurations.

3.4.Fracture surface roughness characterization

To characterize the surface roughness of the macroscopic fractures generated after specimen failure,3D coordinates defining the fracture surfaces were acquired using a high-accuracy profilometer 3D laser scanner (Kreon Zephyr? 25).The fracture surface morphologies of the granite and mortar semi-samples after specimen failure are shown in Fig.9a and b for B1 and Fig.9c and d for D1.Because the interface surface morphology of the mortar part matched well with that of the granite part,only the roughness parameters of the mortar semi-samples were analyzed further,which were subject to the greatest level of damage.

Fig.9.Interface surface roughness geometry of generated macro fractures for (a) B1: mortar,(b) B1: granite,(c) D1: mortar,and (d) D1: granite.

Fig.10a and b illustrates the distribution of the absolute values of asperity heights over the mortar surface for B1(corresponding to Fig.9b) and D1 (corresponding to Fig.9d),respectively.The minimum,maximum,mean,and standard deviation (SD) of asperity heights are shown in Fig.10a and b.In addition,the roughness parameterz2,the root mean square of the first deviation of the roughness profiles (Tse and Cruden,1979),and the fractal dimension,D(Belem et al.,1997),were calculated.Higher values ofz2 andDindicate a rougher surface.Note that the roughness parameters were calculated only along the fracture-propagation direction (i.e.the Y-axis in Fig.9).

Fig.10.Histogram of absolute asperity height over the fracture surface for(a)B1 and(b)D1.The minimum,maximum,mean,and standard deviation of asperity heights as well as the z2 values are given in(a)and(b).Average power spectra(red lines)of the fracture surfaces of(c)B1 and(d)D1 are shown.Blue lines represent the power spectra of a 2D profile extracted from the corresponding fracture surfaces.The Hurst exponent(H)and fractal dimension(D)values are indicated in(c)and(d).All roughness parameters and plots suggest that the fracture surface was rougher in the specimen subjected to direct tension than that subject to the Brazilian tensile test.

To determineD,Hurst exponents (H) were first computed for the 2D roughness profiles extracted from the fracture surface along the Y-axis.Values ofHfor the entire fracture surface were then obtained by stacking and averaging all the 2D Fourier spectra.After determining the averageHfor each surface,the corresponding fractal dimensions were calculated asD=2-H(Belem et al.,1997;Candela et al.,2012).

Fig.10c and d shows the typical average power spectra of the fractured surfaces of B1 and D1.The blue lines represent the spectra of the individual roughness profiles,the black lines represent the maximum and minimum limits,and the red lines indicate the average power spectra of the fracture surfaces.Corresponding H values were obtained as the slope of the linear fit of the red graph.More details on z2,the Hurst exponent,and the fractal dimension can be found in Tse and Cruden (1979),Belem et al.(1997),and Candela et al.(2012).

For B1,z2 and D values were 0.1 and 1.34 (Fig.10a and c)compared to 0.23 and 1.47 for D1(Fig.10b and d),respectively.The interface surface roughness geometries (Fig.9) and their corresponding asperity height distributions,z2,and D values (Fig.10)suggest that the surface of the fracture in D1 was rougher than that in B1.As previously discussed,the fractures in the Brazilian specimens (e.g.B1) were mostly formed by the initiation,propagation,and coalescence of non-tensile microcracks.In contrast,the fracture in D1 was predominantly composed of tensile microcracks.This was further confirmed by the fracture surface roughness characteristics (z2,D,and asperity heights) of these specimens.It has been previously shown that tensile fractures are generally rougher than shear fractures.For instance,Vogler et al.(2017)investigated the surface roughness characteristics of shear and tensile fractures from crystalline rock and reported that shear fractures have lower roughness values than tensile fractures.

4.Discussion

4.1.Tensile behavior of rock-mortar specimens under direct and Brazilian tensile tests

The direct tensile strength of the rock-mortar specimens was 66% of their Brazilian tensile strength,which is similar to the reported ratios for the intact rocks (Perras and Diederichs,2014).In Brazilian loading,a compressive load is applied to the specimen,and the rock-mortar interface is subjected to compression-induced(indirect) tension.However,a tensile load is applied to the specimen under direct tensile loading,and the rock-mortar interface is subjected to a directly induced tension.From a macroscopic perspective,the interface is subjected to tension under both direct and indirect tensile loading,but this is different at the microscale.In our previous work,this difference in the cracking mechanisms under micro-and macro-scales has also been observed for intact mortar and granite specimens (Shams et al.,2023).

The DIC strain fields in Fig.4 and the AE source mechanisms in Fig.7 indicate that both tensile and non-tensile (compaction and shear)microcracks contributed to the formation of macro-fractures in the Brazilian specimens(i.e.B1).Fig.4e shows that at failure,the maximum value of γmax(660 με)was comparable to the maximum value of ε1(1090 με).Moreover,Fig.7 indicates that at failure,the microcracks were composed of 27% tensile cracks and 41% shear cracks.In contrast,the DIC strain fields in Fig.6 and the AE source mechanisms in Fig.8 show that only tensile microcracks occurred in the specimens subject to direct tension (i.e.D1).Fig.6d shows that,at failure,the maximum value of γmax(300 με) was substantially lower than the maximum value of ε1(980 με).Moreover,86% of the microcracks were tensile (i.e.almost all AE events),with no contribution from shear-type cracks (Fig.8).

Based on these findings,microcracking occurred predominantly via the tensile mode(e.g.86% tensile compared to 14% non-tensile AE events,Fig.8)for the rock-mortar specimen tested under direct tension (i.e.D1).In contrast,microcracking occurred predominantly via the non-tensile mode(27% tensile compared to 73% non-tensile AE events in Fig.7) for the rock-mortar specimen tested under Brazilian loading(i.e.B1).The different contributions of tensile and shear microcracks to the formation of the final macro-fracture can,therefore,explain the differences between the tensile strengths of the rock-mortar interfaces under different loading states.

Previous studies have reported that the tensile strength of brittle materials is often less than the shear strength and much lower than the compressive strength (Griffith,1924;Liao et al.,1997;Perras and Diederichs,2014;You,2015).Likewise,microcracks have a lower resistance to tension than to compression and shear.Thus,the higher contribution of non-tensile microcracks in the Brazilian experiments (73% for B1 against 14% for D1) led to higher tensile strengths in the tested rock-mortar specimens(Fig.2).This indicates that rock-mortar interfaces that experience confining pressure show higher tensile strength than those under lower or zero confinement.

In general,fractures propagate according to the principle of minimal energy.This means that fractures follow the easiest paths in the rock,particularly if the available energy is not high.As shown in Fig.2,under Brazilian loading,the accumulated strain energy was higher than that in the direct tests,as a greater loading was required to induce failure.Indeed,under Brazilian loading,the input energy was higher,which in turn resulted in higher energy release.This high released energy can easily break the cohesive bonds and create a straight fracture with less tortuosity(see Fig.9a and b).On the other hand,for the specimens under direct tension,the input and released energies are both low;therefore,the fractures find the easiest path with minimal energy.This means that the fracture will deviate significantly and,thus,result in a jagged surface and a tortuous path for the rock-mortar interfaces under lower or zero confinement (see Fig.9c and d).

Fig.11 shows the typical failure modes of rocks in terms of Mohr circles and envelopes (Hoek and Martin,2014).The induced stresses along the rock-mortar interfaces under Brazilian loading resemble the confined tension failure mode (blue circle in Fig.11).In this case,there is normal compressive stress over the microcracks (owing to the biaxial stress field in the Brazilian test),resulting in higher shear strength values along the microcracks.Therefore,the presence of more shear microcracks with higher strengths during the failure process in B1 increased the overall tensile strength.In contrast,the stress states along the rock-mortar interfaces under the direct tensile test were equivalent to the uniaxial tension failure mode (red circle in Fig.11).In the uniaxial tension failure mode,there was no compression or confinement over the microcracks (owing to the applied external load).Therefore,the shear strength along the microcracks was minimal (as shown by the red circle in Fig.11),highlighting the minor role of shear microcracking in the overall failure and tensile strength of specimen D1.This suggests that the rock-mortar interfaces show higher strength under confined tension than those under unconfined tension.

Fig.11.Stress states for typical failure modes of rocks (Einstein,2021;Hoek and Martin,2014).In Brazilian specimens,normal compressive stress acts over the surfaces of microcracks due to the applied compressive load,meaning that these microcracks may be produced under the confined tension failure mode(blue circle).In contrast,microcracks in specimens under direct tension are predominantly produced in the uniaxial tension failure mode(red circle).Microcracks that fail under confined tension(Brazilian)have greater strength than those that fail under unconfined tension.

4.2.Limitations and future studies

In this study,a constant Vp field model was applied to determine the spatial distribution of AE events.This is because both granite and mortar showed similar Vp values.However,owing to the heterogeneity of granite (different grain sizes,pre-existing cracks,etc.) and the presence of two different propagation media(i.e.rock and mortar),this assumption may not always apply and result in AE location errors.Although our velocity sensitivity analysis showed that this error was negligible for the materials tested,to localize AE events more accurately,a 3D velocity model that considers both the inherent and stress-induced anisotropy of rock is required.

In addition,only specimens with a smooth interface surface were considered when evaluating the tensile strength and tensile fracturing behavior of the rock-mortar specimens.To generalize these results,further experiments should be conducted on rockmortar specimens considering different interface roughness.In this study,the mortar had a lower strength than granite;therefore,most of the fracturing processes occurred either in the interface or the mortar.Testing bi-material interfaces with different mechanical properties of the rock and mortar/concrete is also needed to explore how cracks initiate and propagate for cases in which rock has lower strength,or the two materials have the same strength.The geometry and size of the specimens may affect the tensile strength of the rock-mortar interfaces,which are also needed to be investigated.

AE and DIC techniques should be employed in other tensilemode fracture mechanics tests of rock-mortar specimens to gain further insight into fracturing behaviors.For example,the progressive rock fracture mechanism in cracked-chevron-notched Brazilian discs of rock-mortar interfaces should be studied to determine the Mode I fracture toughness of bi-materials(Dai et al.,2015;Wei et al.,2022).Further work is also needed to examine the effect of tensile loading type,specimen shape,notch type,and interface geometry on the fracturing and mechanical properties of rock-mortar interfaces (e.g.fracture process zone (FPZ),cracking mechanisms,and fracture toughness).The experimental and numerical investigations conducted by Wei et al.(2021)and Wei et al.(2022) provide useful examples of such work.

5.Conclusions

We investigated the tensile strength and failure behavior of rock-mortar specimens under direct and indirect tensile loading conditions.AE and DIC techniques were employed to evaluate the microcracking mechanisms of the rock-mortar specimens.Based on the obtained results,the following conclusions can be drawn:

(1) The DTS/BTS ratio of the rock-mortar specimens was 66%,which falls within the reported range of ratios for intact rocks.

(2) Monitoring the cracking processes in the rock-mortar interfaces revealed that when failure occurs under confined tension,AE precursors are observed before failure,both in terms of timing and spatial distribution.However,significant AE activity may not be detected before failure under direct tension.

(3) The stress state was an essential factor affecting the fracturing mechanisms and the tensile strengths of the rockmortar specimens.The AE and DIC results indicate that microcracks were predominantly non-tensile for specimens under confined tension (Brazilian) and predominantly tensile in those subjected to direct tension.

(4) Due to different fracturing mechanisms,the surfaces of the ultimate macro-fractures were rougher in the specimens tested under direct tension than those tested under indirect tension.

(5) The findings of this study can aid in understanding when,where,and how fracturing happens in the rock-mortar interfaces and whether we see precursors before the catastrophic failure,which are essential factors for successful structural health monitoring in engineering structures.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

The first two authors would like to thank the Natural Sciences and Engineering Research Council (NSERC) of Canada for funding this research program and the Fonds the Recherche du Québec-Nature et Technologies (FRQNT) for financing the research infrastructure.The authors would also like to acknowledge Mr.Danick Charbonneau and Mr.Jean-Christophe Lacasse,technicians at the Rock Mechanics Laboratory of the University of Sherbrooke,for their valuable cooperation.The authors are also grateful to Correlated Solutions,Inc.for kindly providing us with a free license for DIC software.Thanks also go to Mr.Alex Loignon for his support in setting up the DIC system.

Appendix A.Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.jrmge.2023.04.013.