Rock Engineering and Rock Mechanics: Structures in and onRock Masses Alejano, Perucho, Olalla & Jimnez (Eds)

2014 Taylor & Francis Group, London, 978-1-138-00149-7

Quantifying the discrepancy in preloads estimated by acousticemission and deformation rate analysis

M. KarakusSchool of Civil, Environmental and Mining Engineering, The University of Adelaide, SA, Australia

ABSTRACT: In situ stress measurement prior to mining operations is an imperative stage in designing under-ground structures. The measurement will allow engineers to ensure stability of the underground structures byselecting an appropriate excavation techniques and adequate support systems. Direct in situ stress measurementtechniques (e.g. flat-jack) are difficult to implement and require underground access. On the other hand, indirecttechniques such as acoustic emission (AE) and deformation rate analysis (DRA) can be used to estimate thein situ stress reliably from the cored rocks in the laboratory. However, there are some inconsistencies foundbetween measured and estimated stresses using AE and DRA. This paper aims to investigate the accuracy ofboth techniques and provide comparative study in predicting previously applied stresses. Hawkesbury sandstonesinstrumented with AE sensors and strain gauges for DRA were tested under cyclic uniaxial compression loading.Accuracy of the predictions from both methods was compared with the preload (15 kN) and the discrepanciesbetween these two techniques were identified. Felicity Ratio (FR) from AE tests ranged from 0.91 to 1.12 for thefirst loading cycle and 0.89 to 1.17 for the second loading cycle. It was observed inAE analysis that discrepanciesbetween the first and the second cycles increase due to the memory fading effect, which were also prominentlyseen in DRA analysis.

1 INTRODUCTION

Knowledge of magnitude and orientation of in situstress in rock masses has a crucial importance ingeomechanics. Fairhurst (2003) emphasises that dis-tribution of forces is a significant component ofunderstanding basic geological process such as platetectonics and earthquakes as well as designing engi-neering structures in rock masses. However, stressmeasurement, in principle, faces with an obstacle assuch that stress is not a physical phenomenon that canbe measured directly. Therefore, in order to determinestress in a finite body, a relation in the form of stress-strain is required (Fairhurst, 2003). Common stressmeasurement techniques suffer from deficiencies andlimitations (Seto et al., 1997; Seto et al., 1999). Forexample, overcoring and hydraulic fracturing are usu-ally expensive and time consuming techniques, whichrequire highly skilled technical staff. Measuring in situstress in remote areas at great depth in which accessfrom large boreholes and mine workings are hard isone of the deficiencies of these techniques. In order toapply flat jack technique, measurement should be con-ducted at the excavation surface where the rock massis overstressed due to stress concentration, hence, jackpressure may not represent in situ stress.

Unconventional non-destructive techniques (NDTs)have been proposed to estimate in situ stresses fromcored rocks recovered at depths in order to remove lim-itations and deficiencies with the conventional stressmeasurement techniques. Kaiser effect involving

acoustic emission (AE) (Kaiser, 1953), differentialstrain analysis (DSA) or differential strain curve anal-ysis (DSCA), anelastic strain recovery method (ASR)and deformation rate analysis (DRA) (Seto et al.,1999) are amongst unconventional stress estimationtechniques. These techniques basically utilises dam-age and memory effects and will be discussed inthe next sections. The aforementioned measurementshave a significant use in mining, civil and petroleumengineering. Any advancement in low cost optionsis of a great benefit in mining, civil and petroleumengineering.

The paper is structured as such that in section2, theory of Kaiser Effect (KE) and DRA analysisare examined. Section 3 describes the experimentalmethodology that was used to estimate previouslyapplied stresses by both AE and DRA. In section 4results and evaluations of the laboratory tests are dis-cussed and discrepancies between these techniqueswere presented.

2 REVIEW OF ACOUSTIC EMISSION ANDDEFORMATION RATE ANALYSIS

2.1 Acoustic emission

When rock material is subjected to loading and thepreviously applied stress is exceeded, irreversible dam-age occurs in the rock. At this peak stress value, dueto the number of micro-cracks manifested by AE hits

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Figure 1. Point of inflexion in the second loading cycleindicating maximum stress, m in uniaxial cyclic loading(After Lavrov, 2003).

drastically increases as illustrated in Figure 1. KaiserEffect (KE) is the manifestation of damage due tooccurrence of micro-cracks, which is also the signa-ture of a memory of the maximum previously appliedstress in a material, first discovered by Joseph Kaiserin 1950s. Yuan and Li (2008) describe the KE asthe absence of detectable acoustic emission eventsuntil the load imposed on the material exceeds thepreviously applied stress level.

The KE can be recognised as an inflexion (changeof slope) in the cumulative AE hits versus stress (orload) curve as shown in Figure 1. The curve may beapproximated by two straight lines to locate maximumstress level (Lavrov, 2003).

There are some factors affecting AE sensitivity onin situ stress measurement, which were reported byvarious researchers (Yamshchikov et al., 1994; Setoet al., 1999; Villaescusa et al., 2002). Lavrov (2003)investigated influence of time delay and loading rate,effect of rotation of principal axes, and coring processon AE activity. It was reported that loading rate did notinfluence the Kaiser effect but no conclusive resultswere found for time delay (Lavrov, 2013).

Villaescusa et al. (2002) used AE and DRA analysisto estimate the in situ stresses from cored rocks. Six20mm cylindrical samples undercored from a singlediamond drilled core were subjected to cyclic load-ing. Rock samples were loaded 5 times up to a stresslevel accounting depth of the core and uniaxial com-pressive strength (UCS) of the rock with a 0.125 MPa/sloading rate.The difference betweenAE and DRA esti-mation of in situ stresses varied from 5 to 24%. Aresearch similar to Villaescusa et al. (2002) conductedby Tuncay and Ulusay (2008) reports that if AE testsunder uniaxial loading conditions are performed on sixcores with different orientations and KE levels in eachtest are determined, the completed stress tensor can beinferred. This assumes that the KE level determined

from an oriented specimen under uniaxial loading isequal to the normal stress component in its loadingdirection in the earths crust.

Li and Nordlund (1993) found that most rocks(among the tested rocks, marble, gneiss, granite,gabbro, chalcopyrite ore, greenstone and porphyry)exhibit an obvious KE. However, iron ore usuallyshows a poor KE. In order to support estimation ofin situ stresses by KE, DRA analysis should also beconducted.

Chen and Tham (2007) studied the directionaldependence of the KE and they reported that exper-iments performed on uniaxially loaded square platespecimens of brittle granite have demonstrated thedirectional dependency of the Kaiser effect.Yoshikawaand Mogi (1981) also reported that there is no orvery little influence of the loading rate on the KE inShinkomatsu andesite for loading rates in the rangeof 0.005 to 0.3 MPa/s.

As reported by Seto et al. (1997), AE activity thatoccurs on the interface between the sample and load-ing end-platens during testing granular materials is aserious problem. In order to eliminate this AE activity,they used a 0.15 mm thick sheet of polyethylene placedbetween the ends of samples, while Mori et al. (2009)used stiff paper. A 10 mm thick plate of Bakelite wasinserted by Li and Nordlund (1993) at each end of thespecimen to block the noise from the hydraulic systemof the testing machine.

Seto et al. (1997) used an AE monitoring sys-tem comprising a 4-channel NF-9600 Local Processorcapable of recording the full range ofAE parameters aswell as performing two-dimensional source location.Unander (2004) used a combined conventional ana-logue system and a digital transient recorder. Jin et al.(2009) used SAMOS acoustic emission monitoringsystem. AE signals detected by sensors were ampli-fied by a preamplifier (Model 801, Gain= 40 dB,frequency filter range: 1002000 kHz).

The KE can be recognised as an inflexion (change ofslope) in the dependency cumulative AE hits versusstress. In order to determine the value of m moreaccurately, the curve may be approximated by twostraight lines (bilinear regression). The point of theirintersection projected onto the stress axis indicates theKE stress level (Lavrov, 2003).

Data of various investigations have shown theaccuracy of determining the stresses that actedearlier using cyclical uniaxial compression of rockspecimens vary from 5 to 20% (Yamshchikov et al.,1994; Kurita and Fujii, 1979).

Lehtonen et al. (2012) compared results from theirAE stress results on cores from drill hole data to datafrom the overcoring and hydraulic fracturing measure-ments.The results have been transformed to secondaryprincipal stresses on the horizontal plane to help com-parison, where the KE results follow the trends ofthe results obtained by the more conventional over-coring and hydraulic fracturing techniques. It has tobe noted that the directions of the KE results havelarge deviations, the major principal stress differs by

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Figure 2. Schematic illustration of Deformation Rate Anal-ysis a) Loading cycles b) axial differential strain curvesbetween cycles, c) bending point between cycles (Yamamoto,2009).

2030 from the overcoring results which makes themincomparable.

2.2 Deformation rate analysis

In situ stress estimation by DRA analysis was initiatedby Yamamoto et al. in 1990. Earlier work that laid thefoundation of this method was a method called dif-ferential strain curve analysis (DSCA) by Stricklandand Ren (1980) that is also extension of differentialstrain analysis (DSA) introduced by Simmons et al.(1974). DRA uses the principles of the KE where strainis recorded under uniaxial cyclic loading. The differ-ence in inelastic deformation in a specimen betweentwo successive loading cycles was used to determinethe previously applied stress. The strain differencefunction j,i() is defined as:

where, is the applied axial stress and i() is thereduced axial strain for the ith loading. j,i() isapproximated by a straight line with a positive gra-dient at stresses less than the previous peak stress thatrapidly bends at or near the previous peak stress to havea negative gradient as shown in Figure 2c (Yamamoto,2009).Yamamoto et al. (1990) states that this negativegradient at applied stresses is higher than the previ-ous peak stress indicates that the rock specimen canbe easily deformed in the first loading than in the sec-ond one of two successive loading cycles. This is dueto the specimen enlarging pre-existing cracks and/orto create new cracks at its first experience of a higherstress being applied.

Yamamoto et al. (1990) reported that DRA is practi-cally effective for in situ stress estimation as the valuesof previous stresses estimated by DRA indicate theabsolute values of the normal components of the in situ

stress field. The mechanical behaviour of pre-existingcracks in a rock specimen causes, more or less, non-linear strains with respect to the applied axial stress.The frictional sliding is expected to occur on a pre-existing shear crack when the shear stress exceeds acritical value. An isolated tensile crack may open orclose elastically according to the change in the axialstress (Yamamoto et al., 1990).

Wang et al. (2011) studied mechanism of deforma-tion memory effect in the layered rock in the low stressregion and they concluded that the stress relaxation inthe first unloading, delay time and the initial stage ofsecondary loading cause loss of accuracy in the stressdetermination from the first DRA inflexion point dueto memory fading.

The change in the density of the tensile crackchanges the effective elastic moduli of the specimento introduce a non-linear but elastic response to theaxial stress (Walsh, 1965). This kind of behaviourin strain is considered to be mainly reversible dur-ing many cycles of loading, as far as the pre-existingcracks do not change their size (Holcomb and Stevens,1980; Stevens and Holcomb, 1980; Kuwahara et al.,1990). The reversible components of strain are can-celled by the operation of Eq. 1.The axial stress appliedto a rock specimen may enlarge some of pre-existingcracks and create new cracks. Considering what theKaiser effect implies, this should happen especiallywhen the applied stress exceeds the peak value ofprevious stress. The strain resulting from this phe-nomenon is irreversible for two successive cycles andnot cancelled in the strain difference function definedby Eq. 1. From the above consideration, Yamamotoet al. (1990) reports that the use of the strain differencefunction has the advantage of emphasizing the irre-versible component of the measured non-linear strainby eliminating the reversible component. Yamamotoet al. (1990) also states that using the strain differ-ence function we can detect more easily a bendingpoint of stress-strain curve to estimate the peak valueof previously applied stresses. As can be seen fromFigure 2 2,1() bends approximately at the axialstress denoted by in which no artificial stresses hadbeen applied to the specimen before the first load-ing. is considered to indicate the value of in situstress to which the rock sample was subjected at thesite. Tamaki and Yamamoto (1992) commented thatthe gradient changes were not commonly determinedin the stress-strain relations obtained by conventionaltechniques in the case of small previous stresses asthe change is buried in the large nonlinearity of thestress-strain relation resulting from other sources, forexample, crack or pore closure.

3 EXPERIMENTAL WORKS

AE and DRA tests were carried out using Instron1342 servo controlled hydraulic testing machine with300 kN load capacity. The Instron controller consistsof hardware components and software applications

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Figure 3. Triaxial test data of Hawkesbury sandstones.

Figure 4. Applied loading cycles during the tests.

Figure 5. Typical load-strain curve recorded during uniaxialcyclic compressive loading.

that provide closed-loop control of servo-hydraulic testequipment. This machine consists of a compressionloading frame, an axial dynamic loading system and adata acquisition system. The data acquisition systemconsists of a signal conditioning, and an acquisitionunit interfaced with a computer. Multiple or single dataacquisition processes can collect data on all channels.This machine is able to perform cyclic test in both loadand displacement control modes.

Figure 6. Stress vs. cumulative AE hits.

A random selection of 5 Hawkesbury sandstonesamples with diameters of 42 mm and lengths of101 mm whose triaxial data was plotted in 1 3plane in Figure 3 were subjected to uniaxial cyclicloading to a pre-specified load at a constant loadingrate to record AE signals. Test set up and equipmentused in the experiments are illustrated in Figure 4.Mechanical properties of sandstones were determinedover 28 samples. According to uniaxial compressiontests average compressive strength, c is 27.3 MPawith a 3.74 MPa standard deviation.This indicates thatstrength of Hawkesbury sandstone is not varying sig-nificantly. Tensile strength of sandstones was foundto be 1.9 MPa with a 0.57 standard deviation. Triaxialtest data evaluated using RocData in which we foundcohesion, c is about 7.84 MPa and internal frictionangle is 41 degree.

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Table 1. AE results and the discrepancy between appliedand estimated stresses (Prestress= 10.827 MPa).

Estimated Felicity Ratiostress, MPa Discrepancy, % (FR)

Test C-1 C-2 C-1 C-2 C-1 C-2

1 11.19 11.12 3.33 2.67 1.033 1.0272 11.33 11.4 4.67 5.33 1.047 1.0533 12.13 12.41 12.0 14.67 1.120 1.1474 11.48 12.63 6.00 16.67 1.060 1.1675 9.89 9.67 8.67 10.67 0.913 0.893

Table 2. DRA results summary and discrepancy betweenloading cycles (Prestress= 10.827 MPa).

Estimated stress, MPa Discrepancy, %

Test A2-A1 A3-A1 A3-A2 A2-A1 A3-A1 A3-A2

1 11.12 11.55 11.77 2.67 6.67 8.672 11.04 10.97 10.61 2.00 1.33 2.003 11.26 11.19 11.33 4.00 3.33 4.674 10.83 10.97 10.11 0.00 1.33 6.675 11.55 11.40 10.18 6.67 5.33 6.00

Loading rate of 3 kN/min were used for the cyclicloadings shown in Figure 4 where the samples wereloaded to a 15 kN preload for 10 minutes. Thespecimens were then subjected to three cycles of load-ing; the first cycle is up to 15 kN and second andthird cycles are up to 20 kN. The AE monitoringsystem consisted of three AE sensors connected tothree amplifiers, which were connected to a triggersignal generator with a NI PCI-6133 data acquisi-tion unit. Frequency bandwidth of AE pico sensorsis 200 kHz800 kHz. Recording and visualisation ofsignals were done using a signal processing softwaredeveloped in house using Labview. Sets of 2/4/6 seriesfilters with 20/40/60 dB gain single ended differen-tial preamplifiers were used to amplify signals 60 dB.The system recorded AE events above the thresholdvalue of 100 mV, recording 100 readings each timethe 100 mV was triggered. Axial strain, lateral strain,and the corresponding loads were recorded simultane-ously. Figure 5 shows applied cyclic loading and axialstrain during testing.

4 DISCUSSIONS AND CONCLUSIONS

Approximately 40% of the compressive strength ofHawkesbury sandstones, 15 kN preload for all testswas chosen. The load and its corresponding hit timeswere labelled 1 to n so that the load against the cumu-lative number of hits could be plotted for the 015 kN(cycle 1 (C-1)), 020 kN (cycle 2 (C-2)) and 020 kNloadings (cycle 3 (C-3)). As examples, results from

Figure 7. Results of DRA analysis.

tests 1 and 3 can be seen in Figure 6, where we canobserve the point of inflection in the graph as 15.5 kNfor test 1. In the initial loading, it was noted that in situstress could be observed as there is sudden increase ofAE activity before the applied preload. This is of inter-est though there is no data to validate the results. Inaddition, uncertainty about the time delay, orientationand depth of samples from the ground makes harderto confirm in situ results.

The results of the AE visual observation are givenin Table 1. It can be seen that the preload was observedwith a discrepancy range varying from 12.0% to8.67% in the first cycle and 16.67% and 10.67%in the second cycle. Memory fading from first tosecond cycle was around 23% to 38.9%. Differentialaxial strains along the loading direction in betweentwo consecutive cycles against corresponding loads

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are plotted in Figure 7. Axial strain difference betweenthe cycles was taken between cycles 2 and 1; 3 and 1;3 and 2 denoted as A2-A1, A3-A1 and A3-A2 respec-tively. Complete test results are summarised in Table2 with the corresponding discrepancies.

The discrepancy percentages are calculated againstthe stress of approximately 10.827 MPa, which isequivalent of 15 kN load for 42 mm diameter spec-imens. It can be seen that the discrepancy rangedfrom 0% to 6.67% for DRA analysis in betweenfirst and second cycles. In the consecutive cycles, thediscrepancy was increased as shown in Table 2.

Points of inflections for all tests, which indicatemaximum stress, are very clear at cycles between 1and 2, and 1 and 3 as can be seen from Figure 7.However, as indicated by Wang et al. (2011), mem-ory fading occurs after second cycle and thus locatingpoint of inflection in between third and second cycleis very difficult. In conclusion, it is strongly suggestedthat use of both techniques should be considered forcrosschecking of estimated in situ stresses.

ACKNOWLEDGEMENT

Author would like to thank Ian Cates and Sam W.Pattullo for their help during lab tests.

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