back analysis of grouted bolt.pdf

5
 Technical note Back analysis of grouted rock bolt pullout strength parameters from eld tests Bin Li a,, Taiyue Qi a , Wang Zhengzheng b , Longwei Yang c a School of Civil Engineering, Southwest Jiao Tong University, Chengdu, Sichuan 610031, PR China b School of Civil Engineering, Dalian University of Technology, Dalian, Liaoning 116024, PR China c China Railway Erju Co. Ltd., Chengdu, Sichuan 610031, PR China a r t i c l e i n f o  Article history: Received 24 February 2011 Received in revised form 5 October 2011 Accepted 17 November 2011 Available online 10 December 2011 Keywords: Rock bolt Ultimate pullout capacity Bond cohesive strength Friction angle Dichotomy a b s t r a c t This paper focuses on the grout cohesive strength and the grout friction angle of rock bolt, which have a signicant inuence on the pullout force and are difcult to estimate. Traditional method estimate the two parameters from the results of pull-out test conducted under different conning pressures. St. John and Van Dillen gave two approximate empirical formulas in 1984. In this text, a new method was pro- po sed to ba ck ca lcula te the gro ut cohesi ve str eng th and the gr out fri cti on ang le bas ed on giv en e ld pul l- out force of rock bolt. In order to verify the method, a numerical model was built by FLAC 3D to approach the two par ameters by the pr inc ipl e of dic hot omy. The conve rge nce res ult had bee n pro ved to be rig ht by numerical pull-out tests.  2011 Elsevier Ltd. All rights reserved. 1. Introduction Rock bolts have been used widely in many kinds of engineeri ng for a long time. The ultimate pullout capacity determined in eld pull-out tests is the most important parameter of rock bolt. There ha ve be en num erous the or eti cal stu die s tha t address ult i- mate pullout capacity and the application of rock bolt. For exam- ple,  Kilic et al. (2002)  investi gate d the effe cts of the mec hani cal properties of grouting materials on the pull-out load capacity of a fu lly gro uted bolt . Merield and Smi th (201 0) p rese nted the u lti- ma te up lift capa city of multi- plat e strip anch ors in undr aine d clay . Li and Stillbor g (19 99) devel oped thr ee ana lyt ica l models to describe the me cha nic al cou pli ng at the int er fac e be twe en the bo lt and the grout medium for grouted bolts. Cai et al. (2004) estab- lis hed an analy tic al mo de l to pr edict ax ial lo ad in gro ute d ro ck bo lt for soft rock tunneling. In contrast, determination of rock bolt pullout strength param- eter s (i.e. , grou t cohe sive strengt h and the gro ut frict ion angle) attracts muc h less attention. Altho ugh St. John and Van Dillen (1984)  gave some formulas about the grout properties, described in great details in the user’s manual of FLAC 3D , grout friction angle is not considered in their formula. In addition, the only strength parameters considered in their formula (i.e., cohesive strength) is not easy to be determ ined accu rate ly, as it is highly related to the quality of the bond between the grout and rock. However, grout cohesive strength and the grout friction angle ar e two ke y inp ut pa rame ter s to de ter mi ne ult imate pullo ut cap ac- ity of rock bolt when carrying out numerical analysis. The idealization of grouted-cable system is illustrated in  Fig. 1 and ke y inp ut pa rame ter s of ro ck bo lt or gr out are sho we d as follows: (1) G rout mas s dens ity q (op tio nal nee de d if dy nam ic mo de or gravity is active) (kg/m 3 ). (2) Young’s modulus of rock bolt,  E  (GPa). (3) Grout cohesive strength (force) per unit length,  c  g  (MPa). (4) Grout friction angle,  u  g  ( ). (5) Grout stiffness per unit length,  k  g  (N/m 2 ). (6) Grout exposed perimeter,  p  g  (m). (7) Cross-sectional area of rock bolt,  A  (m 2 ). (8) Compressive yield strength (force) of rock bolt,  F c  (N). (9) Tensile yield strength (force) of rock bolt,  F t  (N). Since the shear resistance parameters of the interface between grout and rock and the interface between grout and cable are not described in FLAC 3D , we only discuss the shear resistance parame- ters of the grouting material in this paper. The area, modulus and yield strength of the cable are usually readily available from handbooks, manufacturer’s specications, etc. The grout properties are more difcult to estimate. The grout annulus is assumed to behave as an elastic-perfectly plastic solid. As a result of relative shear displacement  u t , between the tendon surf ace and the bor eho le surf ace, the shea r for ce,  F t , mobiliz ed per length of cable is related to the grout stiffness,  k  g . 0886-7798/$ - see front matter  2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.tust.2011.11.004 Corresponding author. E-mail address:  [email protected] (L. Bin). Tunnelling and Underground Space Technology 28 (2012) 345–349 Contents lists available at  SciVerse ScienceDirect Tunnelling and Underground Space Technology journal homepage:  www.elsevier.com/locate/tust

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  • tanPR CPR C

    Dichotomy

    roue puesupprgroderprin

    in mat capacparamtical stcationthe effthe pu

    in great details in the users manual of FLAC , grout friction angleis not considered in their formula. In addition, the only strengthparameters considered in their formula (i.e., cohesive strength) isnot easy to be determined accurately, as it is highly related tothe quality of the bond between the grout and rock.

    described in FLAC , we only discuss the shear resistance parame-ters of the grouting material in this paper.

    The area, modulus and yield strength of the cable are usuallyreadily available from handbooks, manufacturers specications,etc. The grout properties are more difcult to estimate. The groutannulus is assumed to behave as an elastic-perfectly plastic solid.As a result of relative shear displacement ut, between the tendonsurface and the borehole surface, the shear force, Ft, mobilizedper length of cable is related to the grout stiffness, kg.

    Corresponding author.

    Tunnelling and Underground Space Technology 28 (2012) 345349

    Contents lists available at

    ro

    w.eE-mail address: [email protected] (L. Bin).a fully grouted bolt. Merield and Smith (2010) presented the ulti-mate uplift capacity of multi-plate strip anchors in undrained clay.Li and Stillborg (1999) developed three analytical models todescribe the mechanical coupling at the interface between the boltand the grout medium for grouted bolts. Cai et al. (2004) estab-lished an analytical model to predict axial load in grouted rock boltfor soft rock tunneling.

    In contrast, determination of rock bolt pullout strength param-eters (i.e., grout cohesive strength and the grout friction angle)attracts much less attention. Although St. John and Van Dillen(1984) gave some formulas about the grout properties, described

    3D

    (2) Youngs modulus of rock bolt, E (GPa).(3) Grout cohesive strength (force) per unit length, cg (MPa).(4) Grout friction angle, ug ().(5) Grout stiffness per unit length, kg (N/m2).(6) Grout exposed perimeter, pg (m).(7) Cross-sectional area of rock bolt, A (m2).(8) Compressive yield strength (force) of rock bolt, Fc (N).(9) Tensile yield strength (force) of rock bolt, Ft (N).

    Since the shear resistance parameters of the interface betweengrout and rock and the interface between grout and cable are not

    3D1. Introduction

    Rock bolts have been used widelyfor a long time. The ultimate pulloupull-out tests is the most important

    There have been numerous theoremate pullout capacity and the appliple, Kilic et al. (2002) investigatedproperties of grouting materials on0886-7798/$ - see front matter 2011 Elsevier Ltd. Adoi:10.1016/j.tust.2011.11.004ny kinds of engineeringity determined in eldeter of rock bolt.udies that address ulti-of rock bolt. For exam-ects of the mechanicalll-out load capacity of

    However, grout cohesive strength and the grout friction angleare two key input parameters to determine ultimate pullout capac-ity of rock bolt when carrying out numerical analysis.

    The idealization of grouted-cable system is illustrated in Fig. 1and key input parameters of rock bolt or grout are showed asfollows:

    (1) Grout mass density q (optional needed if dynamic mode orgravity is active) (kg/m3).Bond cohesive strengthFriction angle

    2011 Elsevier Ltd. All rights reserved.Technical note

    Back analysis of grouted rock bolt pullou

    Bin Li a,, Taiyue Qi a, Wang Zhengzheng b, Longwei Ya School of Civil Engineering, Southwest Jiao Tong University, Chengdu, Sichuan 610031,b School of Civil Engineering, Dalian University of Technology, Dalian, Liaoning 116024,cChina Railway Erju Co. Ltd., Chengdu, Sichuan 610031, PR China

    a r t i c l e i n f o

    Article history:Received 24 February 2011Received in revised form 5 October 2011Accepted 17 November 2011Available online 10 December 2011

    Keywords:Rock boltUltimate pullout capacity

    a b s t r a c t

    This paper focuses on the gsignicant inuence on thtwo parameters from the rand Van Dillen gave two aposed to back calculate theout force of rock bolt. In orthe two parameters by thenumerical pull-out tests.

    Tunnelling and Underg

    journal homepage: wwll rights reserved.strength parameters from eld tests

    g c

    hinahina

    t cohesive strength and the grout friction angle of rock bolt, which have allout force and are difcult to estimate. Traditional method estimate thelts of pull-out test conducted under different conning pressures. St. Johnoximate empirical formulas in 1984. In this text, a new method was pro-ut cohesive strength and the grout friction angle based on given eld pull-to verify the method, a numerical model was built by FLAC3D to approachciple of dichotomy. The convergence result had been proved to be right by

    SciVerse ScienceDirect

    und Space Technology

    lsev ier .com/ locate/ tust

  • the back analysis of shear resistance parameters, so it will not bediscussed in this paper.

    Fig. 1. Idealization of grouted-cable system.

    346 L. Bin et al. / Tunnelling and UndergroundUsually, kg can be either measured directly from laboratorypull-out tests. Alternatively, the stiffness can be calculated froma numerical estimate for the elastic shear stress, sG, obtained froman equation describing the shear stress at the grout/rock interface(St. John and Van Dillen, 1984):

    sG GD=2 tDu

    ln1 2t=D 1

    where Du = relative displacement between the element and thesurrounding material; G = grout shear modulus; D = reinforcingdiameter; and t = annulus thickness.

    Consequently, the grout shear stiffness, kg is simply given by

    kg 2pG= ln1 2t=D 2As a result, the shear force Ft (Fig. 2) is given by

    Ft kgut 3The maximum shear force per cable length in the grout is deter-

    mined by the relation illustrated in Fig. 3. The values for bondcohesive strength, cg, and friction angle, ug , can be estimated fromthe results of pull-out test conducted under different conningpressures or, should such results not be available, the maximumforce per length may be approximated from the peak shearstrength (St. John and Van Dillen, 1984):

    speak sIQB 4where sI is approximately one-half of the uniaxial compressivestrength of the weaker of the rock and grout, and QB is the qualityof the bond between the grout and rock (QB = 1 for perfect bonding).

    Neglecting frictional connement effects, cg may then beobtained from

    cg pD 2tspeak 5Fig. 2. Shear force/length versus relative shear displacement, us (Itasca ConsultingGroup, Inc., 2005).When researches are carried out on the anchor effect conductedby calculation software such as FLAC3D, the grout cohesive strengthand the grout friction angle are indispensable, rather than the ulti-mate pullout capacity. Consequently, a program was written by

    3DHence, the maximum shear force per length of rock bolt is givenby

    jFmaxs j=L cg rmpg tanug 6

    2. A new method for back calculating strength parameters ofrock bolt

    Grout cohesive strength and grout friction angle could bededuced from pull-out test, which may be time consuming andnot economic. In addition, the measured results may not be reliableas the accuracy of the results is affected by all kinds of factors inmodel test.

    The formula given by St. John is an approximate formula.Besides, the value of cohesive strength is relevant to the qualityof the bond between the grout and rock, which is almost impossi-ble to conrm. Furthermore, St. John had not given a formula toestimate the grout friction angle.

    To address these problems, a new method is proposed to deter-mine the two strength parameters of rock bolt.

    Field pull-out tests are very universal in the application of rockbolt. In these tests, ultimate pullout capacity can be conrmed. Theultimate pullout capacity is specied by Ft in this paper.

    The grouting pressure has a signicant inuence on rock bolt,for example, quality of the bond between the grout and rock, thecompaction rate of grout which causes difference parameters ofgrout. All of the above factors can lead to difference ultimate pull-out capacity. However, the grouting pressure is not important to

    Fig. 3. Shear-strength criterion (Itasca Consulting Group, Inc., 2005).

    Space Technology 28 (2012) 345349FISH, the built-in language of FLAC , to approach the inputtedeld pullout force by varying the grout cohesive strength and thegrout friction angel based on the principle of dichotomy. The the-ory of the program is very similar to FEM Strength ReductionMethod (Grifths and Lane, 1999; Dawson et al., 1999). A nal con-vergence is achieved when the difference between the computedand targeted pullout force is less than a pre-dened tolerance-value and the two strength parameters will be outputted.

    It should be pointed out that the back calculated grout cohesivestrength and the grout friction angle by the program are merelypossible to be the real parameters of the grout, but they are corre-sponding to the targeted ultimate pullout force of rock bolt. So theback calculated strength parameters may serve as relatively rea-sonable input parameters in other relevant numerical analyses.

    Fig. 4 shows three ways to back calculate strength parametersof rock bolt. Line 3 back calculates both the grout cohesive strengthand the grout friction angle. In Line 4, only grout cohesive strength

  • is back calculated based on giving a determinate grout frictionangle (ranging from 20 to 60); Line 1 neglects frictional conne-ment effects (friction angle is set to be 0), and only takes the cohe-

    changed by the principle of dichotomy in the program. Thesetwo parameters can also expressed by their initial value (c0g1; c

    0g2,

    u0g1, u0g2) as:

    cg 0:5 cg1 0:5 cg2 nc0g1 1 nc0g2

    7

    ug 0:5ug1 0:5ug2 nu0g1 1 nu0g2

    8

    The allowable tolerance between Ft and F0 was denoted by d. Itis well recognized that a smaller d value means a more accurateresult, but longer computational time is required to achieve theconvergence.

    The cohesive strength cg and the friction angle ug used in thenumerical simulation will be the target value when the differencebetween Ft and F0 is less than allowable tolerance d, otherwise, thedichotomy will be applied to change cg1, cg2, ug1, ug2 and update cgand ug. Hence, a new pullout force F0 will be acquired in numericalsimulation by using the updated parameters, and a new compari-son between Ft and F0 will be conducted again. The cycle will notstop until the difference between Ft and F0 is less than d.

    3. Example

    A numerical model was built in FLAC3D to implement out idea.Fig. 6 shows the three dimensional mesh of the nite differencemethod. The dimension of the model is 3 m 10 m 3 m. In the

    Fig. 4. Shear-strength criterion for convergence.

    L. Bin et al. / Tunnelling and Underground Space Technology 28 (2012) 345349 347sive connement effects into consideration.Line 2 in Fig. 4 represents the actual relationship between the

    conning pressure and pulling force per meter of rock bolt. The lineis xed by conducting pull-out test under different conning pres-sures (at least two kinds of conning pressures). The intercept andslope of the line represents the grout cohesive strength andtangent of the grout friction angle, respectively.

    Regardless of which kind of way was chosen, the same pulloutforce will be obtained from line one to line four under the sameconning pressure. The ow chart of the back analysis programis illustrated in Fig. 5.

    In the back analysis, the grout cohesive strength and the groutfriction angle are varied based on the principle of dichotomy. Eachnumerical run gives a different combination of grout cohesivestrength and the grout friction angle and hence a pullout force ofrock bolt. The program will keep running till the differencebetween the computed and the targeted pullout force is smallerthan a given allowable tolerance.

    Ft is the pullout force from eld pull-out test and F0 is the pull-out force from numerical simulation by using the grout cohesivestrength cg and the grout friction angle ug. The grout cohesivestrength cg is the average value of the lower limit cg1 and the upperlimit cg2, while the grout friction angle ug is the average value ofug1 and ug2. The initial value of cg1, cg2, ug1 and ug2 (c0g1; c0g2, u0g1,u0g2) will be set by programmer at the beginning. The lower limitand the upper limit of these two strength parameters will beFig. 5. Block diagram of the back analysis program.Table 2Parameters of rock bolt.

    YoungsmodulusE (GPa)

    Cohesionc (MPa)

    Groutstiffnessper unitlength kg

    Tensileyieldstrength(kN)

    Frictionangle u()

    D(mm)

    t(mm)Fig. 6. Numerical simulation model.

    Table 1Parameters of rock.

    Deformationmodulus E (GPa)

    Poissonratio l

    Mass density c(kN/m3)

    Cohesion c(MPa)

    Frictionangle u ()

    4.66 0.34 23.00 1.0 33(GPa)

    25 Undened 0.78 250 Undened 64 13

  • numerical model, an 8 m long rock bolt was set at a depth of 5 mbelow the ground surface.

    In this numerical analysis, the rock is modeled by an elasto-plastic model with MohrCoulomb failure criterion. The parame-ters of rock and rock bolt are summarized in Tables 1 and 2,respectively.

    The initial lower limit and upper limit of the grout cohesivestrength are set to be 0 Pa and 1e5 Pa, while the initial lower limitand the upper limit of the grout friction angle are set to be 0 and

    as Ft. The relationship between pulling force of rock bolt and calcu-lation steps is illustrated in Fig. 8. It can be seen that the ultimatepullout capacity varies from 255.14 kN to 215.07 kN after 11 cy-cles. The difference between Ft and F0 is about 0.07 kN, which isless than the given allowable tolerance 0.1 kN.

    The data in Table 3 present the variation progress of parametersbased on the principle of dichotomy and the result of Fig. 9 (series1) and Fig. 10 (series 1) indicate that the grout cohesive strengthvaried from 5e4 Pa to 2.29e4 Pa, while the grout friction angle var-

    Calculation steps (1103)

    Pulli

    ng fo

    rce

    (KN)

    Fig. 7. Initial numerical pull-out test.

    Number of cycles

    Cohe

    sive

    stre

    ngth

    (10

    4 )

    Fig. 9. Variation of the grout cohesive strength.

    348 L. Bin et al. / Tunnelling and Underground Space Technology 28 (2012) 34534990. Hence the two initial parameters used in numerical pull-outtests are 5e4 Pa and 45 respectively.

    The value of the allowable tolerance (d) in this research is set tobe 0.1 kN, which is far less than the pullout force.

    By adopting the two initial parameters, a numerical pull-outtest was conducted, and the relationship between pulling forceand calculation steps is illustrated in Fig. 7.

    As expected, the pulling force of rock bolt increases with calcu-lation steps. The pulling force stops increasing when it reaches255.14 kN. This value is taken as the ultimate pullout capacity ofrock bolt.

    The value of the ultimate pullout capacity from eld pull-outtest is assumed to be 215 kN, which was inputted into the program

    Pulli

    ng fo

    rce

    (KN)Calculation

    Fig. 8. Back analysis progress of the grout cohe

    Table 3Variation of parameters based on the principle of dichotomy.

    Cycle cg1 (kPa) cg2 (kPa) ug1 () ug2 () n (

    1 0.00 100.00 0.00 90.00 0.50002 0.00 50.00 0.00 45.00 0.75003 0.00 25.00 0.00 22.50 0.87504 12.50 25.00 11.25 22.50 0.81255 18.75 25.00 16.88 22.50 0.78136 21.88 25.00 19.69 22.50 0.76567 21.88 23.44 19.69 21.09 0.77348 22.66 23.44 20.39 21.09 0.76959 22.66 23.05 20.39 20.74 0.7715

    10 22.85 23.05 20.57 20.74 0.770511 22.85 22.95 20.57 20.65 0.7710ied from 45 to 20.61 after 11 cycles. The nal grout cohesivestrength 2.29e4 Pa and the nal grout friction angle 20.61 arethe target value.

    However, 20.61 is a relatively small value as the grout frictionangle from the experience. The scope from 30 to 35may be moreapproximate. We choose 30 as the given friction angle and con-duct a numerical pull-out test. The variation of the cohesivestrength is indicated in Fig. 9 series 2. The nal cohesive strengthis 2.08e4 Pa while the grout friction angle is xed 30.

    We neglect frictional connement effects (friction angle is set tobe 0) and conduct another numerical test. The variation of thecohesive strength is indicated in Fig. 9 series 3. The nal cohesivestrength is 2.68e4 Pa while the grout friction angle is xed 0.steps (1103)sive strength and the grout friction angle.

    1 n) cg (kPa) ug () Ft (kN) F0 (kN) Ft F0 (kN)0.5000 50.00 45.00 255.14 215.00 40.140.2500 25.00 22.50 235.10 215.00 20.100.1250 12.50 11.25 116.84 215.00 98.160.1875 18.75 16.88 175.70 215.00 39.300.2188 21.88 19.69 205.31 215.00 9.690.2344 23.44 21.09 220.18 215.00 5.180.2266 22.66 20.39 212.74 215.00 2.260.2305 23.05 20.74 216.46 215.00 1.460.2285 22.85 20.57 214.60 215.00 0.400.2295 22.95 20.65 215.53 215.00 0.530.2290 22.90 20.61 215.07 215.00 0.07

  • relationship between pulling force and calculation steps of rockbolt was illustrated in Fig. 11.

    The nal numerical pullout forces by adopting the three groupsof parameters are 215.07 kN, 215.00 kN and 214.90 kN, respec-tively. Furthermore, the process curves of the three numericalpull-out tests are almost identical. These results prove the validityof the three methods and the outputted grout cohesive strengthand the grout friction angle can be used to instead the real valuein numerical simulation.

    5. Conclusion

    In this study, a new method is proposed to back calculate thegrout cohesive strength and grout friction angle based on a givenpullout force of rock bolt. The back calculated value is not the realvalue, but the numerical pullout force will be the same as the eldpullout force by adopting it. Therefore, the back calculated strengthparameters can be used to instead the real value in other relevantnumerical analyses.

    References

    Cai, Y., Esaki, T., Jiang, Y.J., 2004. An analytical model to predict axial load in groutedrock bolt for soft rock tunnelling. Tunnelling and Underground SpaceTechnology 19 (6), 607618.

    Dawson, E.M., Roth, W.H., Drescher, A., 1999. Slope stability analysis by strength

    Number of cycles

    Fric

    tion

    angl

    e ()

    Fig. 10. Variation of the grout friction angle.

    Pulli

    ng fo

    rce

    (KN)

    L. Bin et al. / Tunnelling and Underground Space Technology 28 (2012) 345349 349Calculation steps (1103)Fig. 11. Verication numerical pull-out test.4. Verication

    To verify the correctness of the program, the three groups ofoutputted data were adopted in the numerical pull-out test. Thereduction. Geotechnique 49 (6), 835840.Grifths, D.V., Lane, P.A., 1999. Slope stability analysis by nite elements.

    Geotechnique 49 (3), 387403.Itasca Consulting Group, Inc., 2005. Users Manual of FLAC3D (Structural Elements),

    pp. 6170.Kilic, A., Yasar, E., Celik, 2002. Effect of grout properties on the pull-out load capacity

    of fully grouted rock bolt. Tunnelling and Underground Space Technology 17(4), 355362.

    Li, C., Stillborg, B., 1999. Analytical models for rock bolts. International Journal ofRock Mechanics and Mining Sciences 36 (8), 10131029.

    Merield, R.S., Smith, C.C., 2010. The ultimate uplift capacity of multi-plate stripanchors in undrained clay. Computers and Geotechnics 37 (4), 504514.

    St. John, C.M., Van Dillen, 1984. Rockbolts: a new numerical representation and itsapplication in tunnel design. International Journal of Rock Mechanics andMining Sciences & Geomechanics Abstracts 21 (2), 75.

    Back analysis of grouted rock bolt pullout strength parameters from field tests1 Introduction2 A new method for back calculating strength parameters of rock bolt3 Example4 Verification5 ConclusionReferences