Shear properties of cemented rock fills

Bob A.Lingga,Derek B.Apel

Department of Civil and Environmental Engineering,School of Mining and Petroleum,University of Alberta,Edmonton,Alberta T6G 1H9,Canada

Keywords:Cemented rock fill(CRF)Shear tests Shear strength Friction angle Cohesion Back fill interface

ABSTRACT Application of cemented rock filling to underground mining could not be separated from the corresponding back fill’s shear strength properties.The shear of cemented rock fill(CRF)-rock wall and the shear interaction occurring within CRFs both have some disadvantageous failure chances.In this study,we tried to investigate the complete shear properties of CRFs using direct shear and triaxial tests of cemented granite rock fill.Large-scale triaxial testing was held to accommodate the large CRF sample.Direct shear testing on the prepared flat and smooth surfaces was assessed with brief conversions and their corrections were used to approximate the shear strength envelopes of CRF joint interfaces.Two types of CRFs with the same aggregate size and distribution but different unconfined compressive strengths(UCSs)due to different mixture designs indicated insignificant differences between their basic friction angles,and also their asperity inclination angles.Nevertheless,investigation between direct shear test and triaxial test showed that the specimen with higher UCS tended to have a slightly lower friction angle but a higher cohesion than the other one.

1.Introduction

Back fill utilization has been increasingly reported for the recent underground mining sector.As economic resources are being found deeper due to the fact that the surface reserves are almost mined out,back fill utilization even incorporates binder materials such as cement in order to provide more strength.While a number of studies have been carried out on the compressive and tensile strengths of cemented back fills,studies on the shear properties and strength of back fills are rarely reported.In regard to the back fill as a stability support,it is argued that there is no really useful stability analysis for design if the shear strength of the product has been calculated incorrectly(Marachi et al.,1972).

In many Canadian underground mines,the use of cemented rock fill(CRF)as back fill material is a common practice(Yu and Counter,1983;Reschke,1993;Shrestha et al.,2008;Emad et al.,2012).Especially in cut-and- fill or blasthole stoping operations,which are usually divided by the primary and secondary stopes,shear properties play an important role(Sepehri et al.,2017a,b).While working on filling the primary stopes,shear interactions occur between the adjacent ore body or rock walls and the placed CRF.A number of studies have verified that stress interaction between the ore body and CRF may be mutually supported(Mitchell,1989;Belem and Benzaazoua,2008).On the other hand,mining advancements from the primary to the secondary stopes are supposed toexhibit shear interaction between the primary CRFand the placed CRF at the secondary stope.In this case,this experiment’s purpose is to assess the CRF-CRF shear interaction.

Shear interaction in the presence of CRF can be separated into interface between CRF-CRFand interparticle of CRF by means of the mass.A case of sliding failure on the CRF’s free-face during the adjacent ore extraction could be the shear interaction between interparticle and/or CRF mass.Fig.1 shows the mining sequence where the shear interactions of CRF mostly take place.

In rock engineering practice,these two shear interactions are simply assumed to be the shear of discontinuity and shear of an unbroken material.Based on this,the direct shear and triaxial tests may be used to investigate the shear properties of CRF.It should be noted that this study treats CRF as a solid mass instead of loose aggregate accumulation.In this experiment,direct shear and triaxial tests were conducted on two different types of samples.Each sample was tested after 28 d of curing age.This time was selected so that the CRF should completely set and represent its optimum shear strength.Direct shear strength of CRF-CRF interface in this study is based on a flat and smooth surface approach.Samples in this study are laboratory-created CRF of granite aggregate rock retrieved from a diamond mine in Northern Canada.

Fig.1.Mining sequence:(a)primary stope mined,(b)primary stope after back filling,(c)secondary stope mined and generated interparticle or CRF mass shear at exposed primary stope,and(d)secondary stope after back filling with CRF-CRF interface shear interaction.

The CRF incorporates a binder which,in setting the CRF,behaves more like concrete or rock than regular compacted or nonconsolidated rock fill.This understanding is important to clarify Barton’s shear strength criteria(Barton,2013,2016)that are used later in this study.Experimental work in this study follows Barton’s shear strength of rock joints experiment instead of his shear strength of rock fill interfaces experiment,which is related to loose or non-cemented rock fill.Despite that the triaxial test of CRF is not commonly conducted due to the limited availability of a large triaxial cell for accommodating large CRF sample size,this study delivers the triaxial results of 152.4 mm(6 in)diameter CRF samples.Further details are given in the following sections.

2.Theory,material and experimentation

2.1.Shear strength criteria

Theoretically,a rock’s shear strength can be expressed with the Coulomb relationship:

where τ,c,σ,and φ are the shear strength,cohesion,normal stress,and angle of internal friction,respectively.For rock joints,it is theoretically using the above equationwithout cohesionvalue,thus Eq.(1)for rock joints becomes

However,Eq.(2)only meets the criteriawhen any joint’s contact is smooth,clean,and planar.Then,the generated shear strength envelope is supposed to be linear.However,in reality,any naturally occurring joint is most likely to undulate.In addition to the fact is that envelope plotting from the shear test is also nonlinear.

Various empirical approximations predicting the nonlinearity of a rock joint’s shear strength envelope due to its naturally non-planar characteristics with curve- fitting were found to be more reliable.The initial attempts to interpret the shear strength of rough joints resulted in a bilinear model of shear strength envelope(Newland and Allely,1957;Patton,1966):

Patton(1966)configured the relationship using deviation of the shear strength envelope of ajoint and φbplus i.The experiment of a wide range of normal stress variations toward a non-planar(artificially controlled undulation)interface sample resulted in a deviating shear envelope plot,in comparison with the smooth surface,which proved Patton’s hypothesis.

Further development of the nonlinear shear strength envelope of a joint from bilinear to be more precise as curvilinear had been claimed(Barton,1973,1976,2013,2016;Barton and Choubey,1977;Bandis et al.,1981;Barton and Bandis,1982):

where JRC is the joint roughness coefficient,JCS is the joint-wall compression strength,JCSnand JRCnare respectively the corrected JCS and JRC based on the length of observed joint,and φris the residual friction angle.

In Eq.(4),JRC and JCS are the first two terms introduced by Barton in his earlier study.Upon the development,in consideration of weathering of the natural joint and the difference between a prepared flat surface and natural surface due to residual shear,Barton and Choubey(1977)substituted φbin Eq.(4)with φras given in Eq.(5).Further,Eq.(6)was developed by Bandis et al.(1981)after Barton and Choubey(1977),where JRCnand JCSnwere used to take into account the field scale effect,rather than the derivatives of JRC and JCS.

Barton(2013)suggested that the curvilinearity of the shear strength envelope was affected by how rock behaves under the stress applied.A series of triaxial tests indicated the brittle-ductile behavior of rock as elastoplastic material bended the shear strength envelope(see Fig.2).

Zhao(1997)proposed an equation(Eq.(7))based on Barton-Choubey’s model(Eq.(5))by adding a correction factor of interface matching factor or joint matching factor(JMC)to the JRC.He considered the field condition when usually the joint interface was not completely matching as a fresh joint.Therefore,he also used the term residual friction angle instead of basic friction angle.

Fig.2.Bending of shear strength envelope due to brittle-ductile transition obtained from triaxial tests result(after Barton,2013).

2.2.CRF samples

Granite aggregate of maximum 50.8 mm(2 in)in this context as the material source was going through particle size distribution(PSD)analysis.In mining practice,any particle size larger than 10 mm is generally defined as coarse aggregate.In this instance,this experimental aggregate consists of 40%coarse and 60% fine aggregate by weight.Fig.3 shows the aggregate size gradation that fits Talbot and Richart(1923)suggested method modified by Swan(1985)fordetermining the cemented back fills’particle distribution,with the exponent value(n)of 0.35.

The CRF mixtures were identified by different proportions of water to cement and the cement content.Like the CRF commonly used in the field,experimentally reproduced CRF used general Portland cement as a binder and also admixture adding.General Portland cement type 10 and admixture MasterSet Delvo were selected.Table 1 lists the detail of these two experimental CRF mixtures in weight.

To meet the standard sample size regarding the nominal maximum aggregate size,the mold with dimension of diameter×length of 152.4 mm×304.8 mm(6 in×12 in)was used(ASTM C192/C192M,2016).Prepared samples for the triaxial test werethen stored at the moisture chamber with relative humidityof 95%-100%and temperature of(25 ± 2)°C;while the samples for the direct shear test were placed indoors.The purpose of dry-cured direct shear samples was to mimic the field condition when joints are mostly dry due to air exposure.As suggested by Barton(1976),the surface condition for the testmaybe dryor wet according to the desired application,and Zhao(1997)also did his experiment with dry samples.

Fig.3.PSD analysis result of the aggregate source.

2.3.Load frame and experimentation

2.3.1.Triaxial apparatus and testing

In the Rock Mechanics Laboratory,University of Alberta,a specially fabricated 152.4 mm(6 in)diameter Hoek triaxial cell by RocTest(2017)was used to accommodate triaxial samples in this study.The loading frames incorporated a 10,000 kN capacity servohydraulic INSTRON machine to generate the axial load and a syringe hydraulic pump ISCO Model 100DX to provide the confining pressure.Data gathered from the test were recorded by a data acquisition system.Fig.4 shows the triaxial cell on the loading frame used in the experiment.

The experiment generally followed the standard method A(ASTM D7012-14,2014).The test was run on a controlled rate of 0.3 mm/min of axial displacement until the sample failed.Three samples of CRF-1 and CRF-2 each were tested under different confining pressures.

2.3.2.Direct shear testing and apparatus

The test utilized the Golder Association direct shear machine with constant normal load(CNL)(Hencher and Richards,1982)in the same laboratory(see Fig.5).The machine incorporated one linear position(LP)transducer for normal displacement,two LP transducers for shear displacement,and one pressure transducer for the shear stress.The two horizontal LP transducers were each placed at one side of the yoke.Test results of three LP transducers and one pressure transducer were automatically recorded by the data acquisition system.

With respect to the limited dimensions of the shear box apparatus,all direct shear samples were further prepared to fit the shear box.Dry-cured cylindrical samples were then cut to be rectangular barswitha78mm×127mm flatandsmoothcontactarea.Theshear direction traveled along the longest cross-sectional dimension.Following the standard(ASTM D5607-16,2016)that 10 times of themaximum asperity height along the shear surface should be the minimum of the least cross-sectional areas,the experiment’s prepared smooth and flat sample’s interface(i.e.with asperity height approaching zero)should satisfy.Bonding the specimen to the shear box was utilizing the plaster of Paris as the encapsulating material.

Table 1 CRFs mix designs.

Fig.4.The 154.2 mm diameter Hoek triaxial cell and 10,000 kN capacity loading frame INSTRON.

The experiment used the multistage direct shear test with the repositioning procedure tocreate three plots of shear-normal stress paths from each of the two samples of CRF-1 and CRF-2.The decreasing nominal contact area was taken into account in calculation of the effective stress due to the increasing shear displacement in each test or the catastrophic damages from the previous test-stage.The expected experimental results are illustrated in Fig.6.Similar approach for rock joints direct shear test in the laboratory was used by Muralha et al.(2014),indicating a slight increase of shear stress along each test-stage as the effect of decreasing contact area.The particular procedure suggested that at least three and preferably more normal stresses(Fn)should be applied for a single joint.

3.Results and discussion

3.1.Interparticle shear strength of CRF

A set of triaxial tests was conducted for a total of eight samples,four samples of each CRF(i.e.CRF-1 and CRF-2).The first test on each sample was set without a confining pressure to get the UCS(σc)of corresponding CRF type.The test results,σc,of CRF-1 and CRF-2 were 3.39 MPa and 9.22 MPa,respectively.Theσcwas also used as the confining pressure(σ3)of next triaxial tests,as the σ3value of the following triaxial tests was supposed to not exceed 45%of the σcvalue.In addition,σcwas also used as the JCS value of Barton’s shear strength input in the next section of this study.Table 2 shows the results of triaxial tests of the experiment.Further,the CRF interparticle shear strength envelope is generated with the Coulomb relationship based on Eq.(1)using RocData 5.0 software.The software is used to best fit the shear strength envelope of each CRF(see Fig.7).

Fig.5.Direct shear machine:(a)schematic,and(b)actual direct shear apparatus.

Fig.6.Example of multi-stage shear test under different CNLs with repositioning after Muralha et al.(2014).

Table 2 Triaxial test results data.

Best- fit cohesions and angles of internal friction from RocData are then put into Eq.(1)to model the Coulomb relationship of both shear strength envelopes of interparticle CRF as follows:

The triaxial result assessed with the Coulomb relationship for the CRF gives an understanding of interparticle shear strength of CRF-1,which has cohesion(c)of 0.761 MPa and angle of internal friction(φ)of 45.9°;CRF-2 has c value of 2.163 MPa and φ value of 42.78°.For the same aggregate size and proportion but different material strengths,it is indicated that CRF-1 has a slightly higher angle of internal friction than CRF-2,but CRF-1 has a lower cohesion compared with CRF-2.

Fig.8 shows the failure angle resulting from the experiment.The CRF-1 sample is shown on the left and the CRF-2 is on the right side of this figure.It suggests that the failure mode of CRF under the shear triaxial test indicates a high angle of failure plane.The high angle of failure plane occurs not only to CRF-1 but also to CRF-2.

Fig.7.Interparticle shear strength envelopes of CRF-1 and CRF-2 by RocData.

Fig.8.Mode of failure of CRF under triaxial test.

3.2.Interface shear strength of CRF-CRF

The three stages of direct shear tests with the applied normal loads are 1 kN,1.6 kN,and 2 kN,respectively,which are applied to the four direct shear samples.Generated normal loads from the hanging weights are assumed given the uniform normal load to the nominal area throughout the test.The plots of shear stressdisplacement are shown in Fig.9.The resulted plots are very similar tothework of Muralha et al.(2014)(see Fig.6).Fig.10 shows the plotting of shear strength envelopes from direct shear test results.

Thus,the shear strength envelopes of the flat and smooth interfaces of CRF-CRF based on Eq.(2)in terms ofand φbare written as.

In this study,the assessment of Patton and Barton’s shear strength criteria was approximated from the artificial tension fracture of corresponding CRF.Considering the nature of the particular CRF,binder-aggregate bonding in granite CRF was assumed weaker than the granite aggregate itself.This assumption was confirmed by the UCS tests conducted on the same CRF and granite samples composing the aggregate component of the testing back fill mixture.The UCS value of tested granite core samples was approximately 120 MPa,while the CRF-1 and CRF-2 had UCS values of around 3-9 MPa.Therefore,the shear failure of the CRF material creates fracture with surface profile where the fracture goes through the cementitious bond but only follows the outline of the granite aggregate pieces.Based on our observations regardless of failure mode,the surface profiles of fractured CRF material are very similar.Therefore,the tested CRF profiles can be obtained using the split tensile concrete cylinder procedure in accordance with the standard(ASTM C496/C496M,2017).The natural joint of granite CRF may be identical to the artificial tension fracture,thereby satisfying with CRF-CRF interfaces as well.

A set of asperity inclination angle(i)measurements was recorded using the profile gage.Then they were captured and computed using the software MB-Ruler to give more precise angle values(see Table 3 and Fig.11).The average ivaluewas back-calculated foreach CRF to model Patton’s shear strength criterion.Combining the average i value with basic friction angle of each CRF from Eqs.(10)and(11)gave Patton’s shear strength of CRF-CRF interfaces in Eqs.(12)and(13):

In the Patton’s model,Eqs.(12)and(13)are basically the first partof the linearenvelope of each CRF type,while Eqs.(10)and(11)are the second part of the linear envelope.This CRF-CRF“smooth and planar interface”experiment indicates a limitation in modeling Patton’s bilinear shear strength criterion in terms of the intersection point between the two linear envelopes determination(see Fig.12).Nevertheless,this direct shear of smooth and planar together with tensile fracture asperity inclination measurements of CRF-CRF interface can still produce φband i.Patton’s experiment claimed that φrwas compared favorablywith φb(always within 1.5°of φb)and both were often identical,while the study of CRF attempted to model the φrwith Barton and Choubey’s φrestimation using

where r and R are the Schmidt rebound numbers on wet joint surfaces and dry flat-smooth surfaces,respectively.

A set of Schmidt rebound number measurements were conducted using an L-type PROCEQ concrete Schmidt hammer and followed by averaging the highest five data as suggested by Barton and Choubey(1977)and Barton(2013,2016)(see Table 4).The corrections for the average r and R values of CRF-1 were both 10.Because of the particular test on CRF-1,neither r nor R could reach the smallest rebound number on the Schmidt(i.e.10).Calculated using Eq.(14),the residual friction angles of CRF-CRF interfaces are

Fig.9.Shear stress-displacement curves of CRF-1 and CRF-2 samples.

Fig.10.Shear strength envelopes of flat and smooth CRF-CRF interfaces.

Table 3 Measurement data of i angle(°).

The estimation of JRC was assessed using a surface profiler to interpret the artificial tension fracture’s profile of both CRFs,by matching them into available graphic and chart methods(Barton andChoubey,1977).TheresultsimplygaveaJRCof20(maximum value).A JRC value of 20 for this experiment seemed obviously to consider the joint surfaces consisting of 50.8 mm or less coarse aggregates.Fig.13 illustrates the coarse nature of the placed CRF in the field.

The JCS estimationwas assumed equal totheσcvalue.Therefore,combinations of residual friction angles(i.e.Eqs.(15)and(16)),JRC values,and JCS values created Barton’s shear strength of CRF-CRF interfaces as(where τand σ′nare in MPa):

Fig.11.The i measurement using profiler.

Fig.12.Patton’s bilinear shear strength envelope.

Fig.13.Back fill underground stope with the laboratory tested CRF showing typical rough and undulating surfaces.

Fig.14 shows the extrapolation of Barton’s shear strength envelopes of CRF-CRF interfaces in this study.The plot is extrapolated by using Eqs.(17)and(18).

Barton’s shear strength assessment shows that the CRF-1 envelope yields earlier than CRF-2,i.e.CRF-1’s transition zones are surpassed earlier than CRF-2 in the same effective normal stress state.In simple terms,CRF-2 is stronger than CRF-1.In the previous Patton’s shear strength assessment,however,it is impossible to determine which CRF type has higher shear strength because intersection points could not be determined when φband i were almost identical.

The situation is understandable because Barton’s shear strength criterion is highly affected by JCS since the logarithmic function has to be multiplied by JRC.CRF-1 has JCS around one-third of CRF-2’s JCS(for CRF-1,σc=JCS=3.39 MPa;for CRF-2,σc=JCS=9.22 MPa).Even when φrand JRC are not significantly differed,Barton’s shear strength criteria and procedure are able to model the shear strength of the CRF-CRF interface from only the direct shear of smooth and planar surface testing.

Analysis of the basic and the residual friction angle differences of the CRF-1 experiments confirms with Patton’s experiment where φrand φbare identical,although in the case of CRF-2,φrdiffers from φbat around 4.75°which is slightly off from 1.5°.It can be concluded that for granite CRF,φrand φbare likely not similar to each other.

A comparison between triaxial test results and direct shear test results are shown in Table 5.The experimental result confirms that the Barton’s shear strength assessment is successful in describingCRF shear property similarly with the triaxial test.The shear strength of CRF-2 is higher than that of CRF-1(in the triaxial test,it is indicated by the higher cohesion;in Barton’s test,it is indicated by the higher envelope),and the friction angle characteristic between them indicates that CRF-1 has a higher friction angle than CRF-2(Barton’s is denoted by residual friction angle).

Table 4 Schmidt rebound number measurement data.

Fig.14.Barton’s shear strength envelopes of CRF-CRF interfaces.

Table 5 The shear properties of granite CRFs.

4.Conclusions

Some general conclusions can be drawn from the results of this study:

(1)Shear interaction within CRF in underground mining practices can be divided into two types:

(i)CRF-CRF interface,which can be assessed with direct shear testing of CRF interface,and

(ii)CRF interparticle bonding,which can be assessed with triaxial testing of intact CRF.

(2)Direct shear testing to assess shear strength envelopes of CRF-CRF interfaces can be done through testing on prepared flat and smooth CRF-CRF surfaces with conversions and corrections,preferably using Barton’s shear strength criteria.

(3)Two types of CRFs with the same aggregate size and distribution but different UCSs indicate insignificant differences either between their basic friction angles or basic friction angle plus the asperity angle.But,the residual friction angle between both may be different.Therefore,it is preferred to use the residual friction angle instead of the basic friction angle in any shear strength assessment of jointed CRF.

(4)There is an indication of CRF shear property where CRF is of different strengths but made from the same aggregate size and distribution:the stronger one tends to have a higher cohesion but a lower friction angle than the other.

Conflicts of interest

The authors wish to confirm that there are no known conflicts of interest associated with this publication and there has been no significant financial support for this work that could have in fluenced its outcome.

Acknowledgements

The authors would like tothank the Universityof Alberta Mining Department teams for their support and guidance.A grateful acknowledgement is given to the Indonesia Endowment Fund for Education scholarship(Grant No.20151112014754/LPDP/2015)for the authors’ financial assistance.