1.Introduction

Rock bolts have been used for over 4 decades in mining and civil Engineering applications as part of a reinforcing system within underground excavations due to their ease of installation,efficiency and relatively low costs(Stillborg,1986).They reinforce rock mass by restraining the deformation around the periphery of the excavation.In this manner,the stresses experienced by the rock mass are transferred to the rock bolt most commonly as an axial load.The proper in situ application of rock bolts is crucial,as improper technique and installation can lead to the loss of lives,poor overall support design and elevated project costs.This highlights the importance in understanding the composition of such a reinforcing element,not only within the overall support scheme when using rock bolt support,but also at the smaller scale in terms of various components that contribute to their behavior and performance.

Local instability issues arise around the material surrounding the excavation zone(i.e.zone of plasticity(Vlachopoulos and Diederichs,2009)or excavation damaged zone(Diederichs et al.,2004)).The stability of the opening depends on the stresses and conditions of the rock mass adjacent to the excavation boundary.Rock support refers to the steps taken and the materials used to maintain the load-bearing capacity of the rock near the opening(Brady and Brown,2004).Support of underground openings covers a wide range of subsets including rock bolts,dowels,cables,mesh,straps,shotcrete,and steel ribs.More specifically within these,fully grouted rock bolts(FGRBs)are paramount as they constitute the most used support in both mining and civil engineering applications(Li,2007).

2.Background

In the simplest form,a rock bolt support system consists of a plain steel rod that is chemically or mechanically anchored at one end and contains a faceplate and a nut at the other end.An FGRB has the entire length of a steel element grouted.This is commonly referred to as the embedded length.FGRBs are proposed to minimize the effect of corrosion on the performance of mechanically anchored rock bolts as the grout provides a protective barrier to the bolts from moisture within the ground.An FGRB consists of a steel bar that can be smooth or deformed(e.g.“rebar”or “thread bar”).The grout can consist of cementitious grout containing mixture of Portland cement and water or resin grout made up of polyester resin and organic peroxide hardener.

During the installation of FGRBs,a load can be applied to the support element by tensioning the bolt at the excavation periphery.Thus bolt can apply a positive reinforcing load at the excavation periphery via the arrangement of faceplate and nut.This type of reinforcement is regarded as active support.However,previous research efforts have indicated that actively tensioning the bolt is not benef i cial for all conditions.This is because in most cases,the length of bolt embedded within the rock mass is not long enough to develop sufficient shear strength to support the loads that it will sustain throughout its lifetime(Haas,1975).Where no reinforcing load is applied at the excavation periphery,a rock bolt will begin to provide support only once the rock mass experiences movement.Under these conditions,a rock bolt is identified as passive support.

Windsor(1997)stated that a reinforcing system comprised of four main elements(see Fig. 1),i.e.rock,reinforcing element,internal fi xture,and external fi xture.As it pertains to FGRBs,the reinforcing element is the bolt itself.The external fi xture is recognized as an arrangement that aids in the load transfer at the excavation periphery,i.e.nut and faceplate assembly.The internal fi xture refers to the medium that transfers the load from the rock to the supportelement.The internal fi xture is of utmost importance to the success of load transfer in a rock bolt system since it provides a coupling interface between the rock and the support element.For the FGRBs,this load is transferred throughout the system mainly in the shear resistance induced along the material interfaces.This shear resistance is made up of chemical adhesion,mechanical interlock between the rebar and grout,and Friction(Serbousek and Signer,1987).These three components of shear resistance are lost in sequence as an FGRB is incrementally loaded,and compatibility of deformation along the interface is lost(Li and Stillborg,1999).The host rock mass will also play an important role in the load applied to the rock bolt.The in situ stress as well as the condition of the rock mass,i.e.joints and excavation-induced fractures,will control the extent of convergence,and therefore,the magnitude and continuity of loading along the bolt.

Another significant factor regarding the loading of rock bolts is the installation orientation in comparison to the rock mass movement vector.In situ rock bolts are loaded due to the movement of the surrounding rock mass.This movement may arise from a variety of sources including shearing along a bedding plane,vertical sagging,squeezing,and dilation of a roof layer(Mark et al.,2002).These loading conditions can result in a combination of coaxial and transverse loading(e.g.shearing),as shown in Fig. 2.The former is often regarded as the support capacity and is routinely assessed by conducting axial pull tests(e.g.ASTM D4435-13e1,2013).

Fig. 1.Components of reinforcing system(modified after Windsor,1997).

Extensive researches have been focused on the mechanics associated with the axial loading of rock bolts(Goris,1990;Benmokrane et al.,1995).Many studies focused on the stress distribution alongFGRB(Farmer,1975;FullerandCox,1975;Serbousek and Signer,1987;Signer,1990).The results of these studies determined that the axial strain distribution along the anchor and shear stress distribution at the anchor-grout interface decay exponentially away from the point of applied load along the embedded length as long as the applied load does not cause incompatibility at the interface.Li and Stillborg(1999)discussed the interface compatibility through the term ‘decoupling front’which denotes the coupled(i.e.segment along which load decays)and decoupled sections(i.e.beyond the shear strength threshold of the interface)along the embedded region of the bolt.This decoupling front moves away from the loading point to the toe end of the bolt as load is increased.

Due to the limitations of conventional Instrumentation used in previous research endeavors,there still exists a lack of understanding in the geomechanical responses of FGRBs at the microscale.Many researches solely captured the load and deflection at a single measurement point along the entire bolt(in most cases a rebar specimen)alignment with instruments such as linear variable differential transformers(LVDTs)and load cells(Cruz and Vlachopoulos,2016).However,the ground in which rock bolts are installed is frequently both anisotropic and inhomogeneous.Therefore,categorizing the response of the support system as a whole in this manner makes it extremely difficult to analyze the load transfer mechanism associated with loading at the microscale.Likewise,it has been shown that the common practice of normalizing bolt capacities should be avoided as longer embedment lengths do correlate with greater capacities in a linear fashion(Hyettet al.,1992).Additionally,in cases wherethe bolt is discretely monitored with strain gages,large sections of the bolt go unmonitored.This leaves unmonitored gaps between instrumented sections of the bolt,which can lead to improperly representing the mechanics in these regions by interpolating between values.In essence,local phenomena might be completely missed if the rebar is not discretely instrumented at the exact location where a significant loading feature/mechanism may occur.Overall,the data from these strain measurements are limited by the amount of discrete strain gages that canpractically be installed on a rebar.This is governed by the amount of space required by each gage,the number of connecting wires required,economic considerations,and time constraints.This lack of spatial resolution with regard to conventional strain instrumentation has given rise to a partial capturing and understanding of the complex mechanical behavior that is completely exhibited.

Fig. 2.FGRB typical loading conditions(modified after Mark et al.,2002).

In this context,an optimal method of monitoring the axial strain along the rebar is necessary to improve the quality of capturing such behavior under laboratory or in situ conditions.One such innovative technique for capturing the strain distribution along the bolt comes in the form of fiber optic sensors(FOSs).Such solutions have been widely used in civil engineering applications as part of structural health monitoring(SHM)(Lanticq et al.,2009;López-Higuera et al.,2011;Barrias et al.,2016)including the use of fiber reinforced polymer(FRP)bars for the long-term SHM of concrete structures(Tang and Wu,2016).Similar technologies have also been successfully developed and used to measure the deformations of steel and glass FRP soil nails(Iten and Puzrin,2010;Hong et al.,2016)and to monitor the responses of underground support elements(Forbes et al.,2014).The latter instrumenting technique utilizes Rayleigh optical frequency domain reflectometry(ROFDR)to capture the strain at an unprecedented spatial resolution of 0.625 mm.This technology was applied with a view to more accurately discern the geomechanisms associated with axially loading FGRBs.

3.Laboratory testing program

A series of pull-out tests was carried out within the structures laboratory at the Royal Military College of Canada(RMCC).Tests were carried out using a 322.41 material testing system(MTS)that was outfitted with two 1-inch(25.4 mm)steel plates and two 1-inch threaded rods to f i x the test specimens in place.These specimens included various diameter-and-length concrete cylinders(which are meant to replicate support embedded in rock),with a precast borehole for grouting rebar element.A steel plate(or attachment steel plate)was fixed to the workbench of the MTS with four 1-inch T-nuts and four 4.75-inch(120.65 mm)long bolts,as shown in Fig. 3.The two threaded rods were fastened to the fixed attachment plate by screwing them into a nut between the MTS workbench and plate(the nut was welded to the bottom of the attachment plate).A second steel plate was used alongside two additional nuts to both f i x the test specimen in place and bear all applied loads(i.e.the load-bearing plate).This set-up allowed axial loads to be applied to the grouted rebar specimens in a controllable manner.

Fig. 4.FOS configuration.

3.1.Rebar specimen preparation

No.6(19.05 mm diameter)Grade 60 rebars of varying lengths,purchased fromDYWIDAG-Systems International Canada Ltd.,were prepared by instrumenting them with ROFDR to conduct the pullout tests.This was done according to the methodology outlined by Forbes(2015)and Forbes et al.(2017).All steel bars were modified with 2.5 mm by 2.5 mm diametrically opposing grooves along the entire length of the bar.The FOS was placed within the grooves,and with the use of an epoxy resin,slight tension was applied to the fiber in order to measure minor compression changes.After this,the sensor was coupled to the steel surface of the rod using a proprietary metal bonding adhesive.The adhesive completely encapsulates the fiber within the grooves and therefore protects the sensor throughout grouting and handling of the rebar.The FOS configuration on the rebar specimens can be seen in Fig. 4,in which[1a],[1b],[2a]and[2b]correspond to logged positions of the optical fiber.The modified rebars(due to the grooves)have theoretically altered yield and tensile strengths of 117.3 kN and 183.1 kN,respectively.

为突出所述方法的优越性,图6所示为主成分分析(Principle Component Analysis,PCA)方法对4种运行状态的分类结果,相对NCA方法存在着较高的误分率,说明了所述方法的优越性.

3.2.Concrete specimen preparation

Fig. 3.Pull-out test set-up used throughout the experimental program.

(3)Rebar tensile failure.

The instrumented rebars were grouted into the various concrete specimens utilizing a kind of cementitious grout consistingof resinbased grout with water to cement ratio of 0.4.This water to cement ratio was chosen as this was found to be optimum in the literature in terms of optimizing the performance of the grout for ease of installation(Goris,1990;Hyett et al.,1992).The rebar was first placed within the borehole,after which the grout was carefully poured in with the rebar extending fully through the concrete cylinder.The specimens were subsequently placed on a shaking table.Tests were performed after 28 d curing period of the grouting of the bolts.A series of the specimens is displayed in Fig. 5.

3.3.Monitoring program

对于中央空调而言，目前普遍情况下的使用是预先设置好主机的工作状态后让其自主运行。首先，对于预先设置的状态是否合理仅靠人为经验或主观判断。在运行过程中，若用户感觉冷或热的时候通常去调节末端设备（如风机盘管）的工作状态，来达到理想效果，而此操作对于主机的运行状况丝毫没有影响；如：空调主机在设置好的状态下运行，用户觉得温度较低就把风量关小或温度调高，而这只是改变了末端的热量交换的设置，并不能让主机输出功率降低，主机仍然在正常制冷输出，这就造成了能量的浪费。

In addition to the instruments described above,the distributed optical strain sensing(DOS)technique based on ROFDR coupled with the rebar specimens monitored the continuous strain profile of the bars.In this testing program,the strain profile was measured at a rate of 1 Hz while load was applied to the rebar at a controlled displacement rate of 1 mm/min.Temperature and humidity of the laboratory were controlled throughout the entire testing program.

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Fig. 5.Pull-out test program.

Fig. 6.Monitoring program used in this investigation.

3.4.Testing schedule

The pull-out tests were performed on specimens that varied in embedment length,grouting material,and borehole diameter.This was done in order to study the significance of these parameters on the response of the support element.Additionally,two specimens were tested without properly preparing the borehole annulus in order to determine the influence of the roughness of the annulus.A complete summary of the tests performed can be found in Table 1.

A detailed schematic of the monitoring program is displayed in Fig. 6.The MTS machine used in the pull-out test was equipped with a 250 kN load cell and 250 mm actuator.This allowed for the applied load and concomitant displacement to be measured respectively.An LVDT was attached to the unloaded end of the specimen in order to measure any slip between the rebar and concrete specimen.Another LVDT was fixed independently of the entire testing apparatus in order to obtain a measurement of the amount of displacement of the testing rig itself.This measurement value was removed from the measured displacement at the loaded end in order to obtain a more accurate reading of the displacement of the rebar.A pair of electric resistive strain gages was placed along the outer circumference of the concrete specimens on diametrically opposing sides.These were utilized in an attempt to measure dilation experienced from the shearing of the rebar along the grout.All instruments were connected to an appropriate data acquisition system(DAQ),which logged all of the parameters at a rate of 1 Hz.

4.Results

For each pull-out test performed,data from the conventional instrumentation(i.e.the LVDTs,load cell,and actuator)were plotted in the form of a load-displacement curve.The specimen load-displacement curve derived from the conventional instrumentation for Test 2 in Table 1 can be seen in Fig. 7a.The results exhibited in the figure represent the applied load measured by the load cell directly.The axial displacement values,however,were determined from the data captured by the actuator,and by the LVDT located at the top of the testing specimen.The actuator measured the entirety of the axial displacement.This included the movement of the testing rig as well as the elongation of the section of the rebar that was embedded within the concrete specimen andthe section of the rebar that extended outside of the concrete form.Accordingly,displacement captured by the top LVDT was removed from the axial displacement captured by the actuator,as this movement can be attributed to the ‘shifting’experienced by the testing rig.Additionally,the elongation associated with the portion of the bolt extending outside of the borehole annulus was removed from the axial displacement reading.In this manner,the axial displacements in all load-displacement curves attained with conventional instrumentation represent the behavior of the system as captured at a single measurement point of the rebar at the borehole collar.

Table 1 Testing outline.

Note:C=Cementitious grouted specimen;R=Resin-based grout.

Test no. Specimen length(mm)Borehole diameter(mm)Borehole prepared Grout 1 100 31 Yes C 2 200 31 Yes C 3 100 31 Yes R 4 150 41 Yes R 5 250 41 Yes C 6 200 31 No C 7 100 31 No C 8 500 31 Yes C 9 700 31 Yes C 10 1000 31 Yes C 11 1000 31 Yes C 12 500 41 Yes C 13 500 31 Yes R 14 550 41 Yes C

Fig. 7.Load-displacement curves for Test 2:(a)Support system response(conventional instrumentation),and(b)Rebar response(ROFDR).

The data obtained from the application of ROFDR to the rebar were also utilized in order to derive a load-displacement response:

An example of the resulting arrangement at the bolt-grout interface under these conditions can be seen in Fig. 12.It is observed that in post-evaluation of the specimen,the rebar had completely detached from the grout annulus.Additionally,the grout had been sheared by the rebar ribs moving across it.These results indicate that considerable movement occurred at the boltgrout interface;approximately 3 mm was captured by the bottom LVDT.Furthermore,the detachment of the rebar from the grout and the existence of grout residue between the rebar ribs indicate a combination of two distinct failure mechanisms(i.e.shearing and radial splitting).

The ensuing load-displacement curve can be seen in Fig. 7b(displacement was deduced using Eq.(1)).In Fig. 7,the shape of the load-displacement curve derived with the use of ROFDR resembles that captured with the use of conventional instrumentation.The initiation of radial splitting cracks of the concrete specimen is successfully manifested in the responses of both the optical fiber and the conventional instrumentation as a change in stiffness.This change in slope occurred at the same applied load in both loaddisplacement curves.

The major difference between the load-displacement curves derived from ROFDR and the conventional instrumentation is the magnitude of the recorded axial displacements.For Test 2(Table 1),the conventional instrumentation captured failure of the bolting system at an axial displacement of 1.7 mm.On the other hand,ROFDRcapturedfailureat176μm.This1.524mm (=1.7 mm-0.176 mm)difference in axial displacement can be attributed to two main factors.First,the axial displacement derived using ROFDR does not take into account any slipping observed at the toe end of the rebar.The LVDT coupled to the bottom of the rebar specimen measured 1.5 mm of axial slip.This axial slip describes the discrepancy between the axial displacements captured with ROFDR and conventional instrumentation.A possible explanation for further discrepancies between the measurements is any additional slipping that may have occurred due to the dilation developing at the bolt-grout interface as radial splitting cracks initiated.This sort of movement is not considered in the response of the optical fiber.Accordingly,the load-displacement curve attained using conventional instrumentation summarizes the response of the entire support system whereas the results attained with the optical fiber summarize the response of the rebar specimen(refer to yellow squares of the system and rebar schematics within Fig. 7).

Selected results attained from the application of ROFDR on the rebar during a pull-out test can be seen in Fig. 8,as captured during Test 2.The results are presented as axial strain along the embedded region of the rebar at selected levels of axial load.The continuous blue arrows in the plots are included to help to visualize the location of the strain readings within the specimen.For all ensuing strain profile figures,the ‘Start at 0.0 m’location in the specimen schematic for pull-out test is the 0.00 m location of the strain readings in the graph.

对上述模型进行数值计算,得到管-土变形及位移分析云图(见图4),在y-z剖面处管-土作用应力分析云图(见图5).

As found in previous studies(e.g.Hyett et al.,2013),it was difficult to apply a pure axial loading onto the grouted rebar.This is attributed to the initial straightening and realignment at the borehole collar that the rebar experiences as load is applied to it.This results in a component of bending associated with the loading(i.e.not pure axial loading).Accordingly,in order to remove this component of bending experienced by the rebar,an average of the strain measured on the opposing lengths of the rebar was taken according to Eq.(2).This is the strain that is depicted in all strain profile results.

The results in Fig. 8a correspond to the strain profile of the embedded section of the rebar as observed in the initial region of the load-displacement curve of the system(i.e.pre-failure region of the load-displacement curve).The strain profiles are displayed at selected applied loads that meet this condition.The strain is seen to generally decayawayfromthe collarof the borehole to the end of the embedded section of the rebar.Furthermore,the jaggedness(i.e.the periodic disturbances)of the strain profiles corresponds well with the spacing of the bolt ribs-as the ribs cause the crosssectional area of the bolt to change.This is similar to the results described by Hyett et al.(2013).The end section of the rebar which extends outside of the concrete cylinder is clearly distinguishable as there is no strain that develops along this segment of the rebar.This is due to the fact that this end of the rebar is free,i.e.limit equilibrium.

Fig. 8.ROFDR strain profile results for Test 2.(a)Rebar pre-failure response,and(b)Rebar post-failure response.

ROFDR was also able to capture the response of the rebar after non-critical post-failure of the system(i.e.the FGRB is still able to withstand further loading),as shown in Fig. 8b.For this test,a brittle failure mechanism caused the concrete to radially split along two visible regions of the concrete cylinder.The radial splitting of the concrete cylinder decreased the radial confinement provided to the rebar by the surrounding grout and concrete.Accordingly,the amount of contact that existed between the rebar and grout was not enough to adequately mobilize the entire shear strength available at the interface(i.e.the rebar and grout were decoupled).The f l at region observed in the strain profile of the rebar near the borehole collar is indicative of the region along the embedment length of the rebar that was no longer coupled to the grout and the efficiency of load transfer along this region decreased.This residual load-bearing capacity of the specimen was mainly provided by the region of the rebar 0.1 m within the embedment length(and further on)that remained coupled to the grout.

5.Discussion

The results obtained from the tests performed on all specimens yielded certain loading trends at the micro-strain scale.Generally,three different behaviors were observed.These behaviors were governed by the three failure mechanisms shown in Fig. 9:

（1）当发电机出现定子绕组单相接地故障时，需要对其进行深入的分析，如果发电机电压网络接地电容电流≥5A时，需要装设动作于跳闸的零序电流保护；反之接地电容电流＜5A时，需要装设作用于信号的接地保护。由于发电机外壳都是接地的，定子绕组绝缘破坏引起的单相接地故障出现的频率较高，基于此发电机容量在100MW以上的，往往应该转设保护区为100%的定子接地保护。

(1)Radial splitting crack failure;

(2)Bolt-grout interface failure;and

This study utilized 200 mm diameter concrete cylinders as these have been previously used in the pull-out tests and have attained good results(Benmokrane et al.,1995).The cylinders simulate the confinement provided to a rock bolt by ‘surrounding in situ rock’.The 25 MPa concrete was cast into 200 mm diameter Sonotubes.The concretecylinders wereallowed a minimum duration of 28 d to cure,allowing the full strength of the concrete to develop.The concrete was tested in the laboratory and was found to have a uniaxial compressive strength(UCS)of 25.4 MPa,and a splitting tensile strength(STS)of 2.6 MPa.The concrete specimens were cast with either a precast 31 mm or 41 mm diameter centered borehole.After the curing period,the boreholes were cleaned with water and roughened with a rotary and percussive drill.Cleaning and roughening the boreholes created a better bonding surface for grouting,and favored decoupling of the bolt-grout interface verse the concrete-grout interface.

The first observed behavior corresponded to specimens of shorter embedment lengths where radial splitting of the concrete cylinder was the governing failure mechanism.For this behavior,the load-displacement curve can generally be broken up into three main regions as depicted in Fig. 10:

(1)An initial quasi-linear region of the load-displacement curve of the system which occurred at low axial displacements.Along this region,the initiation of radial splitting cracks occurred which effectively helped to decrease the stiffness of the system as loading progressed.

(2)A peak load-bearing capacity region where failure of the concrete cylinders occurred.This failure was brought about by the propagation of the radial splitting cracks within the grout and concrete.

Fig. 9.Failure mechanisms.

Fig. 10.Load-displacement curve for Test 2:Support system response(conventional instrumentation).

(3)A residual load-bearing capacity region where the remaining shear resistance present at the bolt-grout interface,as provided by friction,decreased as the rebar was incrementally pulled out of the borehole.

The effects of these expanding radial splitting cracks were manifested as a sudden loss in the load-bearing capacity of the system.This observed failure mode is similar to that detailed by Tepfers(1979).The development of these radial splitting cracks as loading progresses is detailed in Fig. 11a.The radial splitting cracks presented in Test 1 are depicted in Fig. 11b and c.The interaction between the rebar ribs and grout controls the amount of slipping observed throughout loading.As the rebar ribs move alongside the grout annulus,the rebar profile pushes outwards onto the grout and concrete cylinder annulus.The radial component of the force generated by this movement is balanced out by the confinement provided by the grout and concrete cylinder.As the tensile strengths of the grout and concrete are exceeded,radial splitting cracks emerge at the bolt-grout interface.These radial splitting cracks continue to propagate until the concrete cylinders completely fail.

where Ux=lis the stretch of the entire element(l being the whole length in increments of x position);l is the length of the bolt;x is the position along the bolt;εxis the strain measurement at position x along the bolt;and Lεis the spacing between measurement points,i.e.the spatial resolution.

The second observed behavior is associated with specimens where the concrete cylinder remained intact and the bolt-grout interface failed.This was the case for specimens with longer concrete cylinder lengths that made it possible for the system to withstand the effect of radial splitting cracks.As an example,this occurred for Test 9 in Table 1.This behavior is hypothesized to be applicable to specimens of shorter embedment lengths where a high radial confinement exists in such a way that the effects of radial splitting cracks are mitigated.Three main regions are associated with this loading behavior as depicted in Fig. 13:

(1)An initial quasi-linear region at low axial displacements;

The response measured with the optical fiber detailed some general trends throughout testing.Two behaviors observed in the strain profiles along the rebar specimens are depicted in Fig. 18.In the graph,the strain profiles are normalized to their corresponding embedment lengths.For specimens with shorter embedment lengths,where only the frictional component of shear resistance was mobilized,the strain profile linearly decayed within the embedded region of the rebar.This was generally observed for specimens with embedment lengths less than 500 mm.Conversely,specimens with embedment lengths longer than 500 mm were able to mobilize the mechanical interlocking component of shear resistance,thus the strain profiles for such specimens exhibited an exponential decay in their strain profile.The results for the specimens with shorter embedment lengths resembled the linear decay behavior predicted for frictionally anchored rock bolts whereas the specimens with longer embedment lengths depicted the exponential decay behavior.Both strain distribution types have been described by Farmer(1975),Serbousek and Signer(1987)and Li and Stillborg(1999).This exponential decay form became more pronounced as the embedment length of the specimens increased.

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Fig. 11.(a)Radial splitting failure mechanism(modified after Hyett et al.,1992);(b)Radial splitting crack failure for Test 1(side-view);and(c)Radial splitting crack failure for Test 1(top-view).

Fig. 12.Bolt-grout and grout-concrete interface conditions in post-testing for Test 2.

Fig. 13.Load-displacement curve for Test 9:Support system response(conventional instrumentation).

(2)A peak load regionwhere thebolt-grout interface failed;and

(3)A residual load-bearing capacity region where the shear resistance of the system decreased stepwise as the rebar ribs sheared past the grout ridges.

In the cases where confinement is maintained at the bolt-grout interface,a volumetric increase at the bolt-grout interface is resisted and grout shearing occurs.On the other hand,when not enough confinement exists,a volumetric increase at the bolt-grout interface will induce the movement of the rebar up and over the grout ridges(referred to as dilational slip).These two distinct failure mechanisms that are uniquely captured utilizing this technology are shown in Fig. 14.

After the peak load,the system exhibited some ductility,as it was able to maintain a residual load.However,after approximately 12 mm of axial displacement,this residual load-bearing capacity drastically decreased(i.e.from 60 kN to under 40 kN).This pattern continued as loading progressed as can be seen in Fig. 13.This behavior of the system can be attributed to dilational slipping occurring at the bolt-grout interface.As the rebar ribs move past a specific section of the grout where competent frictional resistance was achieved,the rebar slips up and over the grout ridges,and the load-bearing capacity of the system decreases drastically until the rebar ribs are able to interlock again with the next series of ridges on the grout,and the system achieves another relatively constant residual load-bearing capacity.The 12 mm spacing of the rebar ribs was found tocorrespond verywell with length of these steps.These results are akin to those observed by Benmokrane et al.(1995)and Blanco(2012).

Throughout the entire embedded length of the bolt,significant grout residue was found on the rebar(see Fig. 15).There was a distinct gap(1-2 mm wide)observed between the rebar and grout surfaces,signifying that the two materials decoupled during testing.Furthermore,the grout ridges were almost completely fl attened by the sliding of the rebar ribs on the grout surface.These results are indicative of the significant amount of slip that was recorded(i.e.mobilized failure mechanism)and that took place along the bolt-grout interface.Accordingly,failure occurred at the bolt-grout interface through a combination of the two distinct failure mechanisms pictured in Fig. 14.These failure mechanisms are known to govern the behaviors of specimens that apply a relatively high radial confinement to the rock bolt during loading.The same concrete batch was used for all cylinder configurations in the experiments discussed.The radial splitting cracks that started early were able to propagate through the entire length of the concrete cylinder.However,for the longer concrete cylinder,discussed for Test 9,the wedging action created by the ribs was not enough to develop radial splitting cracks as to cause failure of the concrete cylinder.

The final behavior captured was limited to specimens of longer embedment lengths,where failure occurred in the form of tensile failure of the rebar.These specimens were able to exploit the full strength of the steel element.The three main loading regions associated with these specimens were(see Fig. 16):

(1)An initial quasi-linear region where the load-bearing capacity of the system was approached;

(2)A nonlinear region where the rebar yielded and the stiffness of the system decreased;and

建构主义理论认为，学生的学习是根据其已有知识和经验进行主动建构的，并非是其所学知识的被动接受。这一理论突出强调了学生的主体地位，主张每个学生都应以自己的原有经验为基础，去建构新的知识体系；教师教学应该以学生的学为中心，把学生当作学习和信息加工的主体，而教师只是学生学习的帮助者和启发者，重在帮助、引导或驱动学生探索和解决问题。

(3)A peak load region where the rebar failed in tension.

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Fig. 14.Bolt-grout interface failure mechanisms(B-bolt,G-Grout).

Fig. 15.Bolt-grout and grout-concrete interface conditions in post-testing for Test 9.

Referring to Fig. 17,an inspection of the failed rebar detailed no significant grout voids throughout its length.Additionally,the grout was found to be intact and there was no grout residue on any section of the bolt.All these results are indicative that mechanical interlocking between the rebar ribs and the grout was the primary provider of shear resistance throughout loading.

结合新时代推进民兵调整改革，我们采取现地走访、座谈交流、函询统计等方式，对湖南省现有50多个经济功能区民兵建设情况进行了深入调研，也通过电话交流等方式了解了其他一些省份的大致情况，初步掌握了经济功能区民兵建设的现状。

5.1.Rebar strain profile trends

Fig. 16.Load-displacement curve for Test 11:Support system response(conventional instrumentation).

在数学教学中渗透德育是寓德育于智育之中，要将德育目标与数学教学内容所具有的德育因素有机结合起来，组成合理的科学的教学结构，通过教师有目的有意识地教学活动，使德育内容在教学中潜移默化地影响学生，逐步内化为学生的思想品德.

5.2.Grouting material trends

The use of a resin-based grout instead of a cementitious grout generally attained higher load-bearing capacities.Fig. 19 displays the load-displacement behaviors of two tests(Tests 1 and 3)on specimens with an embedment length of 100 mm,which differed only in the grouting material used.The cementitious grouted specimen(i.e.Test 1)was much stiffer than the resin-based grouted specimen.Additionally,the cementitious grouted specimen failed at roughly 40 kN whereas the resin-based grouted specimen failed at 44 kN.This increase in load-bearing capacity witnessed with the use of resin-based grout is likely associated with the inherent stronger material properties of the resin in comparison to the cementitious grout.As the cementitious grouted specimens were loaded,cracking sounds were heard throughout as radial splitting cracks began to propagate at the bolt-grout interface.No audible cracking sounds were heard throughout the loading of the resinbased grouted specimens.Accordingly,no radial splitting cracks developed within the resin-based groutor concrete until the failure of entire system occurred.The stronger material properties of the resin-based grout meant that the grout’s tensile capacity was not exceeded at low applied loads-as it was with the cementitious grout.However,dilation at the bolt-grout interface was still presented,but not as immediate as found in the cementitious grout.This more ductile response made it possible for the mismatch between the grout and bolt ribs to efficiently transfer load from the bolt onto the grout and concrete.However,this build-up of load within the grout and concrete is what eventually caused the concrete cylinders of the resin-based grouted specimens to radially splitaspreviously discussed forthe cementitiousgrouted specimens.

Fig. 17.Bolt-grout and grout-concrete interface conditions in post-testing for Test 11.

5.3.Borehole wall preparation

All of the specimens tested had properly prepared borehole surfaces with the exception of Tests 6 and 7(see Table 1).For both of these specimens,the improperly prepared borehole annulus caused slipping at the toe end of the rebar to take place almost immediately with load applied to the rebar.As can be seen in Fig. 20a,the grout column of the specimen used in Test 6 physically slipped outside of the borehole as load was applied.This proves that failure occurred at the grout-concrete interface.As the borehole was not properly prepared,there were not sufficient irregularities along the borehole annulus for the grout to move into and create an effective bond.In this regard,the borehole had a smooth surface as displayed in Fig. 20a.This meant that the entire loadbearing capacity of the system was provided by the friction presented at the grout-concrete interface.As soon as the shear strength of this surface was surpassed,a specific failure mechanism was initiated and the system was incapable of taking on further load as the frictional interface was fully mobilized.The maximum loads that these specimens were able to sustain were 4 kN and 13 kN,for Tests 6 and 7,respectively(significantly lower than previously discussed tests).

5.4.Borehole diameter trends

It was generally found that utilizing a larger borehole diameter(of those tested in this program)improved the load-bearing capacity of the entire support system.Additionally,the response of the optical fiber attained a more pronounced exponential decay,in terms of the strain profiles as shown in Fig. 21.The specimen with a larger borehole diameter experienced exponential decay of the strain profile whereas the specimen with smaller diameter experienced a linear decay of the strain profile.The specimens with larger borehole diameters had a thicker grout layer surrounding the rebar.The thickness of the annulus(and therefore,the material properties of the grout)made it possible for the system to resist dilational cracks to a better degree than the tests performed on 31 mm diameter borehole concrete cylinders.Essentially,the radial splitting cracks had to propagate through a thicker grout layer.This permitted minimaldilation to take place at the bolt-groutinterface which maintained an effective bond between the rebar ribs and grout ridges at the bolt-grout interface.This made it possible for the mechanical interlocking component of shear resistance to be mobilized more effectively in specimens with a larger borehole diameter;hence the more exponential decay-like behavior was witnessed in the strain profiles of such specimens.

5.5.Embedment length effect

The embedment length of the specimens proved to be the factor that most significantly affected the results.Generally,the loadbearing capacity of the system increased as the embedment length increased.In addition,the embedment length dominated the governing failure mechanism as specimens with shorter embedment lengths had concrete cylinder failure via radial fractures and specimens with longer embedment lengths had rebar failure in tension.

The axial stiffness values of the support system,as derived from the initial quasi-linear region of the load-displacement curves and those derived with conventional instrumentation and ROFDR,are presented in Table 2.The axial stiffness values from the optical fiber results are roughly one order of magnitude larger than that of the results captured using conventional instrumentation.This result is expected as the conventional instrumentation captures the performance of all of the components within the support systemworking together whereas ROFDR simply captures the response of the rebar.

There was little correlation between the axial stiffness values of the system,as captured by conventional instrumentation,and the embedment length of the specimens.However,a correlation is discernible by normalizing the axial stiffness values with respect to the embedment lengths,as shown in Fig. 22a.There is a noted decaying exponential correlation between the normalized stiffness and the embedment length.From the axial stiffness values derived fromthe ROFDR results,it is clear that the values generally decrease as the embedment length increases.The normalized axial stiffness values portray the same exponential decay correlation with the embedment length of the specimens.These correlations are seen in Fig. 22b.

例11 标准状况下,往100 mL0.2mol·L-1的FeBr2溶液中通入一定体积的Cl2,充分反应后,溶液中有50%的Br-被氧化。则通入的氯气的体积是( )。

《国标》的出台对商务英语教学提出了新的要求，只有不断进行教学方法的改革才能满足新时代商务英语人才培养的需要。基于体验学习的《综合商务英语》教学活动设计针对不同的教学目标提供了相应的教学活动选择，利用合适的教学策略，教师可以从中选择适当的活动来提高学生的积极性，优化《综合商务英语》课堂教学效果。本文以体验学习理论为基础阐述了不同商务英语教学活动使用的理据，这在同类研究中是不多见的。然而，这些教学活动在多大程度上有效，是否真的有利于达到理想的教学效果，还有待进一步实证研究的检验。

Fig. 18.ROFDR loading trends.Continuous lines indicate strain profile results for Test 2(representative of shorter embedment length trend).Dotted lines indicate strain profile results for Test 10(representative of longer embedment length trend).

Fig. 19.Load-displacement curves for specimen with cementitious grout and specimen with resin-based grout.

Fig. 20.Bolt-grout and grout-concrete interface conditions in post-testing for Test 6(i.e.the effects of an improperly prepared borehole annulus).

Fig. 21.ROFDR strain profile results(embedded rebar section only):(a)41 mm borehole diameter(Test 5)and(b)31 mm borehole diameter(Test 2).

The strain profile distribution for selected axial loads along the embedded section of the bolt of the 1015 mm long specimen used inTest 10 can be seen in Fig. 23.The strainprofiles show the defined exponential decay behavior.It can also be seen that the strain profiles did not mobilize the entire length of the embedded rebar.At all levels of applied load,the strain profiles were observed to decay to a strain value of zero at a distance of 430 mm through the embedment length of the rebar.This means that roughly 43%of the embedded length of rebar was used to transfer load throughout the system.This 436.45 mm(=43%×1015 mm)length can,therefore,be regarded as the critical embedment length of the support system.Comparable results have also been presented by Li et al.(2016).The critical embedment length is the minimum embedment length necessary to use up the entire tensile capacity of the rebar.For the case of FGRBs,this is synonymous with the length of embedded rebar that is necessary to achieve the peak support capacity under ideal conditions.Knowing this length provides design engineers a guideline to follow in the field with regard to ground support design schemes.This can help to minimize ground falls associated with failure of rock bolts as well as minimize costs of project overhead associated with overdesign.

6.Conclusions

The micro-mechanical response of axially loaded rock bolts is non-trivial,especially within jointed and fractured rock masses.The results included herein successfully utilized conventional laboratory instrumentation alongside a state-of-the-art strain measuring technology with an unprecedented spatial resolution of 0.65 mm.The results attained from this laboratory set-up allowed the analysis of different mechanisms associated with specimens

with varying embedment lengths,grouting materials,borehole annulusconditions,and borehole diameters.Overall,three different behaviors were observed.These behaviors were individually governed by three distinct failure mechanisms:radial splitting crack failure,bolt-grout interface failure,and rebar tensile failure.The use of ROFDR made it possible to capture complex support behavior which could not be captured by conventional meansbefore.Additionally,theimportanceofutilizingthe adequate embedment length was emphasized by the results.It was found that as the embedment length increases,the load-bearing capacity of the support system likewise increases.Conversely,as the embedment length increases,the stiffness values of the system and rebar decrease exponentially.Accordingly,care must be taken in installing these support elements in field,as it may not always be more benef i cial to simply use a longer embedment length.Design engineers should carefully study the predicted loading applied to the system as well as the amount of movement that is expected to occur based on the ground conditions in order to make appropriate design decisions.This includes careful considerations of the critical embedment length for FGRBs,as determined in this investigation.

Table 2 Axial stiffness results.

Test Embedment length(mm)Axial stiffness(kN/mm) Normalized axial stiffness((kN/mm)/m)Conventional instrumentation DOS Conventional instrumentation DOS 1 94 62 733 660 7798 2 183 48 664 262 3628 3 92 29 1063 315 11,554 4 78 21 978 269 12,538 5 245 54 386 220 1576 6 174 - 868 - 4989 7 87 - 834 - 9586 8 503 64 274 127 545 9 540 35 157 65 291 10 1017 36 602 35 592 11 879 33 219 38 249 12 495 48 390 97 788 13 285 33 717 116 2516

Fig. 23.ROFDR rebar strain profile results for Test 10 depicting the critical embedment length for FGRBs.

Fig. 22.Axial stiffness results:(a)Conventional instrumentation,and(b)Rayleigh DOS.

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 influenced its outcome.

来去学校我得拿一个书篮，内中有十多本破书，分量相当沉重。逃学时还把书篮挂到手肘上，这就未免太蠢了。凡这么办的可以说是不聪明的孩子。许多拿篮子逃学的小孩子，人家一见就认得出，上年纪一点的人见到时就会说：“逃学的，赶快跑回家挨打去，不要在这里玩。”若无书篮可不必受这种教训。因此我就想出了一个方法，把书篮寄存到一个土地庙里去。我把书篮放到那地方去，次数是不能记忆了的，照我想来，搁的最多的必定是我。

Acknowledgements

The authors wish to acknowledge the support of the following industrial as well as governmental sponsors:Natural Sciences and Engineering Council of Canada(NSERC),the Canadian Department of National Defense,MITACS,Yield Point Inc.and the Royal Military College(RMC)Green Team.

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