S.S.Hashemi,N.Melkoumian,A.Taheri

Deep Exploration Technologies Cooperative Research Centre,School of Civil,Environmental and Mining Engineering,University of Adelaide,Adelaide, Australia

Full length article

A borehole stability study by newly designed laboratory tests on thick-walled hollow cylinders

S.S.Hashemi*,N.Melkoumian,A.Taheri

Deep Exploration Technologies Cooperative Research Centre,School of Civil,Environmental and Mining Engineering,University of Adelaide,Adelaide, Australia

A R T I C L E I N F O

Article history:

Received 25 March 2015

Received in revised form

4 June 2015

Accepted 9 June 2015

Available online 30 July 2015

Real-time monitoring Experimental investigation Thick-walled hollow cylinder(TWHC) Poorly cemented sand formations

At several mineral exploration drilling sites in Australia,weakly consolidated formations mainly consist of sand particles that are poorly bonded by cementing agents such as clay,iron oxide cement or calcite. These formations are being encountered when drilling boreholes to the depth of up to 200 m.To study the behaviour of these materials,thick-walled hollow cylinder(TWHC)and solid cylindrical synthetic specimens were designed and prepared by adding Portland cement and water to sand grains.The effects of different parameters such as water and cement contents,grain size distribution and mixture curing time on the characteristics of the samples were studied to identify the mixture closely resembling the formation at the drilling site.The Hoek triaxial cell was modi fi ed to allow the visual monitoring of grain debonding and borehole breakout processes during the laboratory tests.The results showed the signi fi cance of real-time visual monitoring in determining the initiation of the borehole breakout.The sizescale effect study on TWHC specimens revealed that with the increasing borehole size,the ductility of the specimen decreases,however,the axial and lateral stiffnesses of the TWHC specimen remain unchanged.Under different con fi ning pressures the lateral strain at the initiation point of borehole breakout is considerably lower in a larger size borehole(20 mm)compared to that in a smaller one (10 mm).Also,it was observed that the level of peak strength increment in TWHC specimens decreases with the increasing con fi ning pressure.

?2015 Institute of Rock and Soil Mechanics,Chinese Academy of Sciences.Production and hosting by Elsevier B.V.All rights reserved.

1.Introduction

Borehole stability analysis is an important issue for researchers in the fi eld of geotechnical,mining and petroleum engineering. Several borehole instability problems during or after the completion of drilling have been reported by a number of exploration companies in Australia.Many of these problems were reported in drilling projects in poorly cemented sand formations at the depth of up to 200 m beneath the ground.The sand production problem,as it is known,has also been observed in weakly bonded sandstones where the debonding of sand grains can be triggered by fl uid pressure and induced stresses leading to the failure of sandstone at the borehole wall(Geertsma,1985;Perkins and Weingarten,1988). The strength of a granular material formation is generated mainly by a natural cementing agent that bonds sand grains together(Al-Awad et al.,1999).

In recent decades,a number of numerical and experimental studies have been conducted on borehole stability in different rock formations.Gough and Bell(1982)showed that,in a large number of vertical oil wells,the orientation of consistent breakouts coincides with the direction of the regional minimum horizontal principal stress.Numerical studies on poorly cemented sand formation by Hashemiet al.(2014a,b)revealed that breakage of weak bonding between sand particles causes instability and sand grains remain intact in the case of a borehole failure.In laboratory conditions it was shown that borehole breakouts grow mainly through radial penetration into the rock mass without any circumferential extension(Lee and Haimson,1993).Haimson and Song(1993) conducted laboratory tests on two varieties of Berea sandstones with 17%and 22%porosity,respectively,and revealed two distinct breakout patterns directly related to the microstructures of these rocks and their different modes of failure.Microscopic observation by Hagin and Zoback(2004)revealed that the fundamental mechanism behind sand production is the growth of small, opening-mode and splitting cracks oriented parallel to the tangential stress,starting very close to the borehole wall and propagating deeper into the matrix with increasing stress.Similarborehole instabilities have also been documented by many other authors(Fischer et al.,1978;Ewy and Cook,1990a,b;Chang et al., 1997;Al-Ajmi and Zimmerman,2006).

Uncon fi ned compressive strength triaxial and thick-walled hollow cylinder(TWHC)tests are two of the most useful laboratory experiments(King,1912;Robertson,1955;Hoskins,1969; Adeyanju and Olafuyi,2011).The geometry of the TWHC allows the application ofvarious load path combinations to simulate stress conditions around boreholes.The classical hollow cylinder approach is not well suited to investigating the stability of poorly cemented formations because,during or subsequent to these tests, the instability of the weak sandstone arch and the grain debonding process in sandy formations cannot be captured.The hollow cylinder tests on an intact rock sample focus mainly on rupture phenomena such as shear and tensile failure(Hall and Harrisberger, 1970;Tippieand and Kohlhaas,1973;Cleary et al.,1979).

In this study,a series of newly designed laboratory tests involving real-time monitoring of the development of breakout in an unsupported borehole was conducted.The paper aims to provide a more accurate representation of the actual behaviour of poorly cemented sands,which will be invaluable in designing appropriate borehole support systems.The tests were conducted on specimens ofpoorly cemented sands prepared in laboratory and the effects of different mixture characteristics(i.e.proportion of sand,cement and water)on their mechanical behaviours were studied by conducting compression tests on solid and hollow cylindrical specimens.

2.Drilling fi eld investigation

Exploration boreholes are usually drilled to uncover potential future mine sites.In many cases,drilling is undertaken through poorly cemented sand formations.Generally,the boreholes are 250-300 mm in diameter and 50-200 m in length,depending on the underground conditions in Australia.This study focuses on solid and TWHC laboratory test specimens based on disturbed samples collected from a problematic drilling site at Burra,South Australia.At this site the sediment above bedrock is heterogeneous, with the shallower layers composed of silt and fi ne sand and the deeper layers transition to dark grey plastic clay.The problematic, poorly cemented sandstone underlies this clayey layer and consists of sand particles with a weak cementation due to the presence of iron dioxide,clay and calcite(Fig.1).Quartz grains are mostly fi ne and sub-angular with random orientations.The yellowish-grey specimens were prepared in laboratory so that their fabric closely resembles that of the poorly cemented sands at the drilling site.

To drill a borehole at this site,different drilling methods have been tried to minimise the risk of borehole failure.In some cases, drilling mud has been used to maintain an open borehole during drilling.However,to conduct further investigation,some boreholes need to remain open for several months after drilling.The air core drilling and reverse circulation drilling methods were used in these cases.These are dry drilling methods and have been conventionally applied to drilling through soft ground in Australia.The cuttings are conveyed to the surface and pass through the sample collection system from where they are collected.Drilling continues with the addition of rods to the top of the drill string.When the drilling string reaches the poorly cemented sand layer,the borehole may collapse ifthe bonding between sand particles is not strong enough to provide stability.According to the reports fromdrilling company, the main factors affecting borehole instability include the low strength of poorly cemented sands which cannot sustain the existing in-situ stress after drilling,and,in few cases,fl uid fl ow due to a con fi ned aquifer near the borehole collapse zone.

Fig.1.Vertical geological cross-section near Burra,South Australia(Hashemi et al., 2014a,b).

3.Thick-walled hollow cylinders(TWHCs)

Hollow cylinder specimens were fi rst used in the early 20th century when the importance of adopting a realistic model was identi fi ed for an underground opening.The opening was located at a depth of 9.5 km and susceptible to collapse due to high in-situ stresses(Hoskins,1969).Since then,a wide range of experimental investigations involving hollow cylindrical specimens has been conducted.Robertson(1955)studied the effect of the inner-toouter diameter ratio on the strength of various rocks.King(1912) analysed the system of fractures that might develop during compressive tests on hollow cylinder specimens under different stress states.Bridgman(1952)performed hollow cylinder tests under different loadings.Pomeroy and Hobbs(1962)examined the strength of hollow cylinder coal specimens.Mazanti and Sowers (1966)studied the behaviour of hollow cylinder granite specimens and the effect of the intermediate principal stress(σ2)on their strength.Ewy et al.(1988)studied the deformation and fracture development in a hard rock around a borehole using TWHC tests.These and other work involving TWHC tests show that the TWHC con fi guration tests are well suited for identifying and investigating both the macro-and micro-properties of different rock types.

Depending on the thickness of a hollow cylinder specimen, stresses that develop in its wall due to the application of uniform stresses can be analysed by two different methods.In a TWHC specimen,the wall thickness,t,which is much smaller in comparison to its inner diameter,Di(i.e.Di＞20t),the stresses that distribute across the specimen walls can be considered almost homogeneous and uniform.This assumption is not fully acceptable in the case of a thick-walled hollow specimen,the wallthickness of which is larger in comparison to its inner diameter.In the latter case,stress distribution is not homogenous in the specimen wall.In many textbooks(e.g.Obert and Duvall,1967;Jaeger et al.,2007) closed form solutions based on the linear theory of elasticity for calculating stresses and strains in both thin-and thick-walled hollow cylinder specimens were presented.For a TWHC with an inner diameter of Di,outer diameter of Doand length of L,subjected to axialforce(F),uniforminternalstress siand externalstress so,the principalstresses at any point at a radial distance r from the centre of the specimen can be presented in cylindrical coordinates as follows(Jaeger et al.,2007):

whereσθθ,σrrandσzare the tangential,radial and axial principal stresses,respectively,which are assumed to be uniformly distributed over the specimen on top and bottom end surfaces(Fig.2).

Fig.2.In-situ stresses on an element at a radial distance r from a drilled borehole centre in polar coordinates.

4.Experimental study

Laboratory test facilities that were used in the current experimental testing comprised the following components:

(1)Specimens that were both of a reasonable diameter and of a borehole wall thickness satisfying the TWHC theory condition (i.e.Di＜20t)were used.Hence,a HQ Hoek triaxial cell of 63.5 mm in diameter and 127 mm in height was utilised.

(2)A servo-controlled axial loading system of 100 kN loading capacity with 0.1 N accuracy was used for applying vertical stress to the specimen.

(3)Although the Hoek cell was originally designed to apply high con fi ning pressures to hard rock specimens,the hydraulic pressure gauge was modi fi ed to allow measuring the con fi ning pressure at very low amounts.An automatic hydraulic machine was used in conjunction with a relief valve and a pressure gauge for applying and maintaining the external con fi ning pressure.Since the maximum con fi ning pressure adopted in the current tests was low(6 MPa),a pressure gauge with an accuracy of 0.01 MPa was used.

The TWHC specimens,consisting of poorly cemented sands, cannot be retrieved from the cell after the destructive tests due to the developmentofa large number ofmacro-and micro-cracks and the debonding of sand particles.In addition,the specimen is attached to the membrane and completely crumbles when moved. Thus,it is not possible to retrieve poorly cemented sand specimens and investigate the failure mechanism of borehole after the test.To address this issue,the triaxial cell was modi fi ed to allow simultaneous capturing of the borehole failure mechanism and the process of sand grain debonding at each time step and at different stress paths.A micro-camera with a 225 pixel per inch(ppi)resolution was installed inside the hollow platen to record the process of sand debonding and borehole breakout.The micro-camera was connected to a personal computer to record the borehole conditions throughout the test.A 60-channel data acquisition system was connected to two additional personal computers for recording and storing data.

Initially,three PVC moulds with a slot on the circumference were manufactured to prepare the specimens.However,during the compaction process,the body of the mould bulged and this deformation prevented the specimens from obtaining a uniform cylindrical shape.An additional problem was observed during demoulding.Since the specimens were very weak,deformation of the mould to release the specimen imparted damage to it.To address this issue,steel moulds were designed and manufactured (Fig.3a).The dimensions of the moulds were 127 mm in length and 62.5 mm in diameter.Two removable steel dowels with the diameters of25 mm and 10 mmwere used together with the moulds. These dowels were embedded in the mould to create the borehole in the specimens.As shown in Fig.3a,to avoid damaging the specimen during de-moulding,the moulds comprised two halfcylinders that were joined together by two screws.In addition, the dowels were wrapped in a plastic fi lm(Mayla plastic)and the inner surface of moulds was lubricated with grease(containing a petroleum jelly mixture and stearic acid)which would not penetrate into the mixture.The bottom platens of the moulds were coated with an anti-rust paint to diminish the effect of lubrication. It was observed that unlike the concrete,the strength of the poorly cemented sand specimens was strongly in fl uenced by the mould conditions.

Kongsukprasert(2003)showed that the strength of poorly cemented sand samples is a function of the density of the mixture. Since there was insuf fi cient space between the mould’s inner wall and the internaldowelto facilitate compaction,a toolwas designed and manufactured to uniformly compact the mixture,as shown in Fig.3b.Each specimen was compacted in three separate layers of equal thickness(42 mm).The compaction energy for each impact was maintained constant and equal to 0.35 N m/cm3,which was calculated based on the applied force of the manufactured compactor.Before placing the next layer,the surface of the previously compacted layer was scari fi ed to increase the interlocking between successive layers.To minimise the bedding error effect for the very top layer,a collar was used allowing this layer to achieve conditions similar to those ofthe lower layers(see Fig.3a).To avoid the initial setting of the cement for all specimens,the compaction time was strictly maintained at 20-30 min.The compaction began when water was fi rst added to the mixture and was completed when the fi nal layer was compacted.

Two sets of cylindrical platens were manufactured from hardened steel and were hardened prior to crushing and lapping.The platens were designed using the fi nite element analysis software ABAQUS 6.11 and loading steps similar to those applied during test conditions were applied to the model(Fig.4).According to the results of simulated platens,the strain of the platens was less than 0.01%with the application of the maximum load of 100 kN.This is far greater than the predicted strength of the specimens.Each platen was designed with a tapered hole,35 mm at the top and 25 mm or 10 mm at the bottom based on the TWHC specimen hole size.In addition,a small base was fi tted to the platen to fi x the camera in the position at a small distance above the specimen.The bottom platens were fi tted with a uniform cylindrical hole of20 mm or 10 mm in diameter,which can be fi tted to the bottom ram of the loading machine.These platens were also simulated in ABAQUS.Sand particles,which were debonded from the borehole walls during the test,were allowed to fall onto the bottom platen.

Fig.3.Apparatus developed to prepare the specimens:(a)Special moulds for preparing TWHC specimens;and(b)Special device for compacting the mixture in the mould uniformly(sizes in mm).

Fig.4.The designed and manufactured top and bottom platens(unit:mm).

Since the specimens were weak enough to simulate the poorly cemented sand at the drilling site,they were vulnerable to disturbance prior to loading.To avoid applying the weight of the triaxial cell to the specimen during the test,a wooden base was manufactured to support the weight of the triaxial cell.Thus,there was no need to apply an externalpressure on the specimens to hold the triaxial set before transferring it to the loading machine.

4.1.Test procedure and setup

The cellwas placed on the wooden base and the bottom hollow platen mounted by the loading machine manually ensured that it can move freely inside the Hoek cell.A thin black membrane was used at the end of the bottom hollow platen to ensure that the LED lights of the camera are not re fl ected during video recording.Both ends of the specimen were then levelled by applying a thin layer of dental paste and,after it had been set,lubricated with a special grease to reduce the friction between the platen and the specimen, thus limiting stress concentration and bedding error.During the setting of the dental paste,the specimen was wrapped in a plastic fi lm to avoid excessive drying of its surface,which could result in the loosening of particles.After the dental paste had been set, precise measurements of the specimen’s weight,height and diameter were taken atthree different points by means ofa calliper.

Measuring the dentalpaste deformations at the top and bottom surfaces of the specimen during the test revealed that the dental paste could withstand,without any noticeable deformation,a force ofup to 100 kN,which is far greater than the strength of the poorly cemented specimen.The results from the preliminary tests on the specimens without capping were not reproducible due to the signi fi cant inconsistency in the results.

The top hollow platen was positioned on the specimen and two sphericalplatens were placed on top ofit to ensure that the vertical stress was uniformly applied to the specimen.Pairs of axial and lateral strain gauges were used to measure local deformations on the specimen.Two linear-variable differentialtransformers(LVDTs) were installed between the top and bottom rams of the loading machine to measure axialdisplacement externally.Prior to the test, the upper machine ramwas brought to the edge of the top platen to set the offsets and 5 N was applied to ensure the contact between the top ram and the hollow platen.The captured image of the micro-camera was checked to ensure that the focal length of the lens was on the middle ofthe specimen hole and the position ofthe LEDs was controlled to ensure the borehole illumination was suitable for recording.In the fi rst stage of loading,the vertical and con fi ning stresses were increased simultaneously up to a certain stress level,which simulates the hydrostatic condition on the specimen boundary.Then,in the second stage,the sample was subjected to vertical compression at a constant displacement rateof 0.07 mm/min.The effects of various strain rates(0.02-0.1 mm/ min)were also examined.No signi fi cant change was observed in the strength and strain behaviours of the specimens within this strain range.Data were recorded at 0.5 s time intervals.

As has been reported by various drilling companies,time is a key factor in predicting the borehole stability after drilling or when withdrawing the drilling rods from the borehole to change the drilling bit.The video capture software was synchronised with the data acquisition system to facilitate the observation of the sand particle debonding process in parallel with the stress and strain measurements.

Several sets of synthetic mixtures of poorly cemented sands were prepared and tested with different cement-to-sand ratios(by weight),wc,coarse-to-fi ne sand particle ratios,δ,and grain size ranges.

4.2.Grain size distribution

To determine typical grain size distributions,samples were collected from the depth of up to 100 m at the drilling site in Burra, South Australia,and sieve analyses were performed using ASTMC-136 calibrated sieves plus pan.The particle size distribution was found to be almost uniform fi ne grained.Based on these sieve analysis results,naturalsilica sands(99.6%ofsilica)oftwo different grain size ranges,closely resembling the ones at the drilling site, were selected for preparing the synthetic mixtures in the laboratory.For these sand grains,the mean diameter(D50)for particle sizes of 0.425-1.4 mm(termed as“coarse”)was 0.56 mm and,for grain sizes of 0.125-0.355 mm(termed as“fi ne”),was 0.20 mm. The coef fi cient of uniformity(Cu=D60/D10)for the coarse and fi ne sand grains was 1.452 and 2.268,respectively.The sands were sieved and packed into plastic bags,about 3 kg in each,to preserve the natural moisture content of the sands.The density of the fi ne and coarse sand particles was 1.47 g/cm3and 1.59 g/cm3, respectively.

4.3.Water content

According to Gueguen and Palciauskas(1992),water content should be kept at a minimum value to avoid segregation of the cement and sand grains.Different water contents were considered to create the most suitable mixture.To determine the optimum water content for the mixture,standard Proctor compaction tests were conducted(Fig.5).These tests were performed on mixtures both with and without cement.Fig.5 shows that the optimum water ratio evaluated by using compactor hammer with energy of 0.55 N m/cm3was achieved at 9.7%-10.3%.There was no signi fi cant change in optimum water content and density in the case of the sand and cement mixture or of the sand grains only.

4.4.Cement content

Portland cement type II(speci fi c gravity Gs=3.15)was used for preparing the TWHC specimens based on previous studies on the mechanical properties of weakly cemented sands(Saidi et al., 2003).The cement powder used in the current study was from a single bag and it was kept in a sealed and airtight container throughout the laboratory studies.

For preparing poorly cemented sands in laboratory conditions,a wide range of wcvalues have been suggested by different researchers(Alsayed,1996;Kongsukprasert,2003;Saidi et al.,2003, 2005).Kongsukprasert(2003)used a maximum of 2.5%of Portland cement,whereas Saidi et al.(2003)used 9%-18%.In addition, Gueguen and Palciauskas(1992)stated that the minimum wcis reached when the coarse-to-fi ne sand particle ratio,δ,is equal to 1.5.Saidiet al.(2005)showed that a very smallamount of Portland cement will increase the strength and stiffness of cemented sand mixtures ifdeposited at grain-to-grain contacts.However,based on the authors’observations,using sands of the above-mentioned grain size distribution,for wc≤2.5%,the specimens could not be successfully de-moulded after the curing time(2-12 days).

Fig.5.Proctor compaction test results of silica sand with and without Portland cement powder(wc=6%).γdis the dry density(g/cm3),and wwis the water content(%).

A number of mixtures with different values of wcandδwere prepared and examined to achieve the apparent mechanical behaviour of the drilling site samples.For the mentioned particle size distribution range,values of wc=6%,7%and 8%were selected. According to the test results,since the grain size distribution signi fi cantly affects the strength of the specimens,it is not possible to create poorly cemented sand samples by using a fi xed wcvalue for different particle size distributions.

4.5.Coarse-to-fine sand particle ratio(δ)

The cement content,wc,and the coarse-to-fi ne sand particle ratio,δ,were varied to obtain the desirable mixture.In this study, since the cement powder particle is fi ner than the sand grains,the cured Portland cement is assumed to be a continuous phase despite the fact that it includes micro-granule and micro-porosity(Saidi et al.,2005).The specimen contains three separate phases:sand, cement and macro-porosity larger than the sand grain size(Ashby and Jones,2014).Scanning electron microscope(SEM)photographs con fi rmed that macro-porosities were often larger in size than the sand particles themselves(Fig.6a).According to Saidiet al.(2005), the minimum macro-porosity is achieved whenδis around 1-3. Also,based on the collected samples from the drilling site,the cured mixture should be weak enough to allow sand particles to debond when the surface is scratched with a fi nger nail.Therefore, different values ofδwere examined for a constant wcto determine the most suitableδ.Finally,δ=1 was chosen based on the test outcomes which are discussed later.

4.6.Curing time

Fig.6.(a)SEM photograph showing that macro-porosities are larger than sand particles in the cemented sand mixture.(b)Borehole breakout occurring in the area which seems to still contain some moisture.

Various curing times have been suggested in previous studies (e.g.Kongsukprasert,2003;Saidi et al.,2003).In the current research,curing times of 2-12 days were examined.The curing time includes the curing ofthe mixture,both in the mould and after de-moulding.In the case of less than 5 days curing,the specimens could not be successfully de-moulded.Preliminary tests were performed on TWHC specimens with total 5 days curing time. Careful examination of the video taken during testing and of the cross-sections of the tested specimens(Fig.6b)revealed that all boreholes had failed in a zone that seemed to have retained some moisture and had not yet completely dried.After further studies, based on the uniaxial compressive strength(UCS)test results,5-day curing was deemed to be the optimaltime for curing inside the mould when the specimen was compacted at atmospheric pressure.After removal of the mould,each specimen was wrapped by plastic fi lm,placed in an airtight plastic container and leftto further curing for another 3 days under atmospheric pressure and at a constant water content.To ensure that 26%-29%porosity was achieved,no externalpressure was applied to the specimens whilst curing.

5.Results and discussion

In order to determine the properties of the mixture,various preliminary tests were conducted on solid and TWHC specimens. The results of these tests can be used to compare other drilling fi elds and ground conditions to those examined in the currentstudy.Preparation of the mixture began with wc=1%using only fi ne grained sands.Table 1 presents the details of the physicomechanical properties that were observed from the uniaxial and triaxial tests.To determine the mechanical properties of the specimens,a number of solid cylindrical specimens with different sand grain size distributions,Portland cement and water contents were prepared.

Table 1 Properties of the prepared poorly cemented sand specimens.

5.1.Effect of coating on the strength of TWHC specimens

Based on the preliminary test results,foil strain gauges and external LVDTs were selected to measure the axial and lateral strains during triaxial testing.To identify the most suitable coating for poorly cemented sands,three specimens with the same characteristics were prepared.Four strain gauges were placed on each specimen with different underlining conditions (i.e.polymer,plastic bond,no lining).The results from the strain gauges using the plastic bond lining and the specimen without lining showed irregularities in the stress-strain diagrams,but the strain gauges placed on the polymer coating showed good and reproducible results and the cohesion of the polymer and specimen continued to be preserved after the test.Thus,polymer coating was deemed to be the best suited option for the subsequent triaxial testing.

Fig.7.(a)Borehole breakout occurring in an area out of strain gauge coating;and(b)polymer application pattern to minimise the effect of coating on the strength ofthe specimens.

Fig.8.Results of UCS tests.(a)Effect of differentδvalues on the strength of poorly cemented sand specimens;(b)Effect of different wcvalues on the stress-strain diagrams and(c)on the volumetric strain,whereεais the axial strain.

In addition,the strengthening effect of the polymer on the poorly cemented sand TWHC specimens was considered.Video recordings that were taken inside the borehole of the preliminary TWHC tests showed that the debonding of sand particles in the specimens initiated in the zone out ofthe applied polymer location (e.g.top and bottom sections of the borehole,see Fig.7a).In the tests without coating,debonding often began uniformly in the middle of the specimens.However,using polymer coating is essential for obtaining accurate readings from the strain gauges,as discussed earlier.To address this problem,in subsequent tests a thin layer of polymer was applied along the length of all the specimens symmetrically as is shown in Fig.7b.The results showed the signi fi cance of using the camera in identifying the factors affecting the process of sand debonding from the borehole wall. rises and the specimens become more brittle in the post-peak regime.The strength of the mixture increases signi fi cantly as δgrows because the coarse sand particles exhibit greater resistance to rotation in the specimen matrix than the fi ne particles.Therefore,when the number of the coarse grains increases,the rotation of particles becomes more dif fi cult due to the improved level of interlocking between the particles after compaction and the global compressive strength of the mixture is increased.In the case of higherδ,the other reason behind the mixture strength growth is the decrease in the special surface of sand particles in the whole matrix which enhances the in fl uence of cementation in the specimen.Therefore,by increasing the sand grain size,it is possible to obtain a higher strength mixture for a certain wcvalue.This confi rms the fi ndings by other researchers(Kongsukprasert,2003; Saidi et al.,2003,2005)who used different ranges of wcto create cemented sand specimens.Also,the level of compaction improved with the increase ofδup to a certain leveland thus the cementing agent could bond more sand particles in a unit volume.

It should be noted that increasingδby more than 1 was not considered in this research,because the aim was to test particle sizes similar to those observed at the Burra drilling site.

5.2.2.Effect of cement content in UCS tests

To study the effect ofcement content(wc),three different values of w c were considered,namely 6%,7%and 8%under the same testing conditions.To examine reproducibility of the results,specimens with 7%and 8%of cement content were tested twice.Fig.8b presents the stress-strain diagrams of the specimens with a dry density of 1.81 g/cm3after 7 days curing.

From the UCS test results,the following trends can be observed: (1)The maximum strength,σmax,and pre-maximum stiffness increase as wcrises.This outcome is in agreement with Saidiet al. (2003)and Kongsukprasert et al.(2005)who used other ranges for wcandδ.

(2)The post-peak stress-strain trend of the specimens with lower

values of wcexhibits greater ductile behaviour.As shown in Fig.8a and b,the UCS is affected to a greater extent by wcthanδ.

The effect of wcon the volumetric strain is presented in Fig.8c.It can be observed that as wcincreases the specimens experience greater axialand volumetric strains prior to failure.In addition,for lower wcvalues,dilation is evident in the specimens after a limited amount ofcompression.However,with increasing cementation the lateral strain decreases and the volumetric strain is affected mostly by the axial compression strain.The axial strain increased by about 83%and 84%atεv=0 with wcincreasing from6%to 7%and from 7% to 8%,respectively.

Furthermore,the effect of water required for cement hydration was considered by increasing the water content in smallincrements within the range of 5%-12%,covering the dry,optimum,and wet sections of the optimum water diagram. Kongsukprasert et al.(2005)showed that,for the cemented sand mixture,the added water cannot be entirely used for cement hydration.The totalwater content of the mixture comprises of a part that serves to hydrate the cement and another part is absorbed by the grains at the time when water is added to the mixture.In addition,Chen and Wu(2013)suggested that the degree of hydration increases as the curing time and water-to-cement ratio of the mixture rise.However,they showed that excessive water content increases the total porosity and results in strength reduction. When the sand grains are not in the saturated-surface dry(SSD) mode,part of the water will be absorbed by the grains,while the remaining part covers the particles’surfaces.Specimens with less than 6%water content could not be de-moulded after even 10 and 12 days of curing time,which inferred that,due to the high speci fi c surface of the sand particles,a minimum of 6%water content was required to achieve hydration.The results showed that,for a speci fi c density of a compacted mixture,the highest strength is obtained with the water content at or around the optimum one,and the strength is signi fi cantly reduced when the water content is less than the optimum value.As mentioned earlier,the optimum water content was determined by standard compaction tests and was found to be almost 10%.

5.3.Triaxial test results on solid specimens

Triaxial tests on solid specimens were performed to determine the shear failure properties of the specimens under different stress conditions.Table 2 shows a summary of the fi nalvalues ofδ,wcand wwwhich were identi fi ed by preliminary tests,whereσconfis the con fi ning pressure.

Fig.9a-c presents the results of the triaxial tests on the solid specimens with different wcvalues.As shown in Fig.9,an increase in con fi ning pressure results in an increase in peak strength. However,the con fi ning pressure has a minimal effect on the stiffness of the specimens.Also,as it can be seen from Fig.9,this material exhibits strain hardening behaviour,i.e.continuous increase in the deviatoric stress with axial strain.Thus,the stress corresponding to 1%of axial strain was considered as the maximum strength of the specimens.The results show that the material behaves nonlinearly even in the early stages of the loading process as was seen by the UCS tests earlier.Paterson (1967)showed that ductility increases with increasingσ3.Fig.9 shows that the ductility of the specimens at lower con fi ning pressures is less signi fi cant and increasing the con fi ning pressure results in the transition from brittle to ductile behaviour.According to the results,for wc=7%and 8%,the elastic strain remains relatively constant due to an increase in con fi ning pressure. Higher con fi ning pressures(e.g.＞6-6.5 MPa)were examined for specimens in each of the three categories and the results showed that strain gauges on the specimens failed at these higher con fi ning pressures.This problem often occurs due to the sandy surface and weak matrix of this material.

Table 2 Schedule of the triaxial tests conducted on solid and poorly cemented TWHC sand specimens.

Fig.9.Deviatoric stress versus axial and lateral strain behaviours of solid specimens subjected to triaxial testing:(a)wc=6%;(b)wc=7%;and(c)wc=8%.

5.3.1.Mohr-Coulomb strength parameters

Mohr-Coulomb criterion is one of the most commonly used ailure criteria in borehole stability problems(Jaeger et al.,2007). oulomb suggested that shear failure will take place when the hear stress is equal to the sum of cohesive shear strength and the roduct of the coef fi cient of internal friction and normal stressacross the fracture plane.Later,Mohr asserted that the relationship between the normal and shear stresses along the failure plane is nonlinear:

where f is a function that can be derived empirically.

To explain the behaviour of the materialby the Coulomb failure criterion,the cohesion,c,and the angle of internal friction,φ,were determined.As expected,increasing the cement content produces higher cohesion between the sand grains,and based on the Mohr-Coulomb criterion,c(cohesion)changes for different cement values.The c andφvalues are presented in Table 1.For different wcvalues,the derivedφvalues show that the angle of internal friction does not change dramatically due to the increase in the cement content.This is mainly due to the grain size distribution not being changed in the specimens tested.

5.3.2.Volumetric strain results

Lateral strain was measured during the triaxial tests on solid specimens to study the effect of con fi ning pressure and cement content on the volumetric strain of the prepared specimens.Fig.10 shows the average values ofthe volumetric strains calculated based on average values of lateral and axial strain gauges for solid and TWHC specimens.As can be seen in this fi gure,at lower con fi ning pressures(i.e.1 MPa and 2 MPa)the solid specimens began to contract fromthe top and bottomsections fi rst and after 0.55%axial compression strain,it diverted to lateral dilation.Increasing the con fi ning pressure kept the specimen in a more contraction mode and dilation began at higher axialstrain values.With an increase in the con fi ning pressure,the lateral strength of the specimens will rise and the lateral dilation will be lower for the same axial strain. As mentioned earlier,after the elastic phase in the stress-strain diagram,the solid specimens exhibited strain hardening behaviour. Thus,for con fi ning pressures greater than 2 MPa,the solid specimens remained in contraction mode and never conjugated the horizontal axis(i.e.the zero volumetric strain)until the maximum strength which was assumed equivalent to 1%of axial strain.The results also show that the effect of varying the cement contents on the volumetric strain is less signi fi cant than altering the con fi ning pressure.For instance,at con fi ning pressures of 1 MPa and 2 MPa, increasing the wcvalue from 6%to 8%does not result in any divergence in the behavioural trend from contraction to dilation in the specimens.

Fig.9 also presents the deviatoric stress versus lateral strain behaviour for solid specimens.It shows that applying higher con fi ning pressure slightly increases the stiffness of the materialin the lateral direction.In addition,the specimens exhibited more brittle behaviour at low con fi ning pressures and,with increasing con fi ning pressure,the materialresponse became more ductile.It is worth mentioning that the specimens underwent lower lateral deformation by increasing the wcvalue at a constant ww,δand con fi ning pressure.

5.4.Triaxial test results on TWHC specimens

Triaxial tests on TWHC specimens were conducted to investigate the borehole breakout and failure properties of the synthetic specimens under different stress conditions.Real-time video recording helped to determine the initiation and direction of borehole breakout and to locate the sand debonding on the borehole wall.The main TWHC tests were conducted for three different cement contents(wc)and for two different borehole diameters: 10 mm and 20 mm.

Fig.10.Volumetric strain versus axial strain results from triaxial tests on solid and TWHC(10 mm borehole)specimens:(a)wc=6%;(b)wc=7%;and(c)wc=8%.

Fig.11 presents the results of the triaxial tests on 10 mm diameter borehole TWHC specimens for three different wcvalues (6%,7%and 8%)and various con fi ning pressures.As shown in Fig.11a,increasing the con fi ning pressure from 1 MPa to 3 MPa signi fi cantly enhances the levelof peak strength and strain energy in the specimens.It should be mentioned that the pre-peak stiffness does not change dramatically with an increase in the con fi ning pressure for a certain wc.However,forσconf＞3 MPa,the levelofthe strength increment is lower than that for the previous states.For con fi ning pressures higher than 4.5 MPa,the fi rst stage of the test (i.e.applying hydrostatic stress to the boundary of the specimens) could not be completed and the borehole collapsed immediately.

Fig.12 shows the process of the borehole failure prior to applying the deviatoric stress.However,the axial strain gauges continued to function even after failure.This emphasises the signi fi cance of using the micro-camera during the borehole stability studies.

Fig.11.Deviatoric stress versus axial and lateral strain behaviours of 10 mm borehole TWHC specimens for(a)wc=6%,(b)wc=7%,and(c)wc=8%,and the effect of the con fi ning pressure on the strength of the specimens.

As shown in Fig.13a,unlike the solid specimen test results,the TWHC specimens did not exhibit strain hardening behaviour after the maximum strength and the peak strength can be determined in the applied stress ranges.Fig.13a shows that the ductility of the specimens increases with an increase in the con fi ning pressure as is the case for the solid specimens.

Also,increasing the cement content by a small amount slightly increases the stiffness of the specimens for the same sample preparation and test condition.

The results show that the con fi ning pressure has a minimal effect on the stiffness as exhibited in the stress-strain curves.This result agrees with that of Mogi(2007)who showed that the yielding stress of ductile rocks does not increase with increasing con fi ning pressure.

5.4.1.Effect of wcandσconfon lateral and volumetric strains

Fig.11 also shows the deviatoric stress versus the average lateral strain for different values of wcand con fi ning pressures.Analysis of the micro-camera video recordings and Fig.11 show that,for a given wc,with an increase in the con fi ning pressure,the borehole breakout initiates at a lower lateral strain and the ductility in the direction ofσconfdecreases.However,as mentioned in the previous section,increasing the con fi ning pressure results in greater ductility.

Fig.10 also shows that,at lower con fi ning pressures(i.e.1 MPa and 2 MPa),the TWHC specimens transit to the dilation mode and with an increase in the con fi ning pressure the borehole breakout initiates in a contraction mode as in solid specimens.This is mainly due to the fact that high con fi ning pressures create borehole convergence and therefore the size of the sample in the lateral direction reduces.Also,due to the presence of a borehole at low con fi ning pressure,the volumetric strain curve conjugates the horizontalaxis at higher axialstrain value in comparison with solid specimens in the same con fi ning pressure,suggesting that microcracks are developing on the borehole wall and sand grain dislocation occurs in the TWHC specimens versus solid specimens to release the applied stresses and return the equilibrium condition to the specimen.In addition,as shown in Fig.10a-c,with an increase in wc,the lateral strain increases compared to the axial strain and prior to borehole breakout in the TWHC specimen,axial contraction of specimens with higher wcis less than that of the specimens with lower cement content.In other words,an increase in wcresults in decrease in the pore spaces of the specimens,and application of the axial deviatoric stress causes less contraction in the axial direction.Therefore,for higher wcvalues,the lateral strain of poorly cemented sand specimens is more dominant in comparison with the axial contraction.Based on the real-time camera recordings,it can be stated that,in the samples where dilation failure happened,the transition from the volumetric strain contraction to the dilation occurred before the borehole breakout initiation.Also for the same specimen condition,increasing the cement value by a small amount slightly increases the stiffness of the specimens under a certain con fi ning pressure(Fig.13b).

5.4.2.Size-scale effect on TWHC specimens

As mentioned above,the TWHC specimens were prepared in two borehole sizes:10 mm and 20 mm.The same process was adopted for the 20 mm borehole specimens,including grain size distribution,curing time,compaction force,and so on.Triaxialtests were performed on 20 mm borehole specimens for different wcvalues and con fi ning pressures.Fig.14a presents the deviatoric stress versus the axialand lateralstrains for 20 mm borehole TWHC specimens for wc=7%and different con fi ning pressures.Fig.14b illustrates the results of the specimens with 10 mm and 20 mm borehole sizes to compare their behaviours.As expected,the strength of the 20 mm borehole TWHC specimens at failure is generally lower than that of the smaller borehole specimens especially at higher con fi ning pressures due to size-scale effect which was shown by Carpinteri(2002).Also,it shows a considerable decrease in ductility for the 20 mmborehole specimens versus that for the specimen with a 10 mm borehole.Fig.14b shows thatthe stiffness of the TWHC specimens does not change with increasing borehole size.This is in agreement with Mogi(2007) who suggested that the stiffness depends on the rock material and,since the same mixtures were used for both specimens with different borehole sizes,the same stiffness was observed from the tests.

Fig.12.Sand dislocation and borehole collapse processes due to the hydrostatic pressure with high con fi ning pressure(6 MPa)prior to the application ofthe deviatoric stress to the TWHC specimen.

Fig.13.(a)Diagram comparing stress-strain behaviour of10 mm borehole TWHC and solid specimens for wc=6%;and(b)Effect ofcement contenton the strength ofthe TWHC specimens for a given con fi ning pressure(σconf=3 MPa).

Fig.14.(a)Deviatoric stress versus axial and lateral strains of 20 mm borehole TWHC specimens for wc=7%;and(b)Diagram comparing stress-strain behaviours of 10 mm and 20 mm borehole specimens for wc=7%.

In lateraldirection,Fig.14a shows that with increasing con fi ning pressure,the lateral strain decreases for specimens with 20 mm borehole and the same wcvalues.In addition,it was observed that under different con fi ning pressures the lateral strain at the borehole breakout initiation point is considerably lower in the 20 mm borehole specimens when compared with the 10 mm borehole specimens(see also Fig.11b).However,the lateralstiffness remains unchanged and is unaffected by the increase in borehole size from 10 mm to 20 mm.Also,the lateral ductility signi fi cantly decreased in the specimens of larger borehole size.In other words,the breakout in the borehole with larger diameter(20 mm)occurred at a lower strain compared to that for a smaller diameter borehole (10 mm).

6.Conclusions

This study has examined the stability of boreholes in poorly cemented sand by a series of newly developed laboratory tests.It was observed that the strength of the poorly cemented sand specimens is largely in fl uenced by the mould conditions.The realtime monitoring of preliminary tests on TWHC specimens showed that in the case of curing the specimens for less than 8 days (ww=10%),borehole breakout initiated in a zone which was not fully dry.At a given wc,the peak strength and stiffness of the specimens increased with an increase in the weight of coarse sand grains.Also,the specimens showed more brittle behaviour for higher levels ofδ.

The post-peak stress-strain behaviour of the specimens with lower wcshowed more ductile trend and the effect of wcwas more considerable than that ofδin the UCS tests.In lower wcvalues, dilation occurred after a limited compression in the specimens and with the increasing cementation the lateral strain decreased and the volumetric strain was mostly dominated by the axial compression strain.

Using the videos recorded during the preliminary test on TWHC specimens,the strengthening effect of the applied coating was investigated and it was found that the borehole breakout started in the area out of the section where polymer was applied.

Solid specimens exhibited strain hardening behaviour and no peak strength was observed in their stress-strain diagram both in axial and lateral directions.Unlike the solid specimens,TWHC specimens did not exhibit strain hardening behaviour after the maximum strength was reached and the peak strength could be determined in the applied stress ranges.

At lower con fi ning pressures(i.e.1 MPa and 2 MPa),solid specimens started contracting initially from the top and bottom sections and after 0.5%-0.6%of axialcompression strain,it diverted to the lateral dilation.Increasing the con fi ning pressure kept the specimen in contraction mode and dilation started with delay at a higher axial strain.For con fi ning pressures of more than 2 MPa, specimens remained in contraction mode and never diverted to the dilatation until the maximum strength was reached.

For the TWHC specimens with con fi ning pressures higher than 4.5 MPa,the fi rst stage of the test could not be completed and the borehole failed before the application of the deviatoric stress.Also, in the TWHC specimens the volumetric strain curve conjugated the axialstrain axis at a higher magnitude which suggested that microcracks were formed on the borehole walland sand grain dislocation took place in TWHC versus solid specimens to release the applied stresses.Based on the observations from the real-time camera recording,it can be stated that the transition from the volumetric strain contraction to the dilation occurred before the initiation of borehole breakout.

The failure strength of the 20 mm borehole TWHC specimens was less than that of the 10 mm ones especially at higher con fi ning pressures due to the size-scale effect.Also,ductility was less in 20 mm borehole specimens in comparison with that in the 10 mm ones.However,the stiffness in axial and lateral directions did not change with an increase in the borehole size.Also,it was observed that the lateral ductility signi fi cantly decreased in the specimens with larger borehole size.

For further investigation on the behaviour of poorly cemented sands,it is suggested to upgrade the laboratory tests to polyaxial stress condition in order to simulate anisotropic horizontal in-situ stresses adjacent to a drilled borehole.

Con fl ict of interest

The authors wish to con fi rm that there are no known con fl icts of interest associated with this publication and there has been no signi fi cant fi nancial support for this work that could have in fl uenced its outcome.

Acknowledgements

This work has been supported by the Deep Exploration Technologies Cooperative Research Centre whose activities are funded by the Australian Government’s Research Programme.This is DET CRC Document 2015/262.

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Dr.Saeed Hashemiis a Lecturer in the fi eld of Geomechanics at CQUniversity in Australia.He received his Ph.D.from the University of Adelaide and his thesis was on“Drilling and maintaining stable boreholes in poorly cemented sands”.Saeed holds a M.S.degree in Geotechnical Engineering from the Sharif University(the highest ranked university in Iran),and a BSc degree in Civil Engineering from Iran University of Science and Technology. He is the author of several journal papers in A+and A journals(Excellence of Research Australia ranking).Saeed has demonstrated experience in lecturing various geomechanics and rock mechanics courses and in supervising student projects at the University of Adelaide and Sharif University.Besides his academic work experience,Saeed also has more than 7 years of industry work experience where he worked on different construction and oil and gas projects.Saeed received several research grants and awards during his career in Australia,such as Joint Research Engagement Engineering Cadetship Grant,Deep Exploration Technologies CRC,etc.Also,he is a permanent member of Engineers Australia and Organisation for Engineering Order of Buildings in Iran.

*Corresponding author.Tel.:+61 426111280;fax:+61 883134359.

E-mail address:shashemi@civeng.adelaide.edu.au(S.S.Hashemi).

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