1975_Stress distribution along a resin grouted rock anchor_F

1、1975_stress distribution along a resin grouted rock anchor_f int.,l. rock mech. mm. sci. geomech. abstr. vol. 12, pp. 347 351. pergamon press 1975. printed in great britain stress distribution along a resin grouted rock anchori. w. farmer* the paper compares theoretical shear-stress distribution alo

2、ng a loaded resin,qrouted rock anchor, with computed shear-stress distributions obtained j?om tests on instrumented anchors in concrete, limestone and chalk. the results show that whilst at lower anchor loads in the concrete, the observed shearstress distribution is similar to the theoretical shear-

3、stress distribution; in the weaker limestone and chalk there is e,idence (? si.qnificant dehondin,q. it is concluded that anchor resistance in these rocks comprised mainly fully mobilised shear resistance. 1. introductionthe recent introduction and widespread utilisation1,2 of resin grouted rock bol

4、ts and anchors in civil and mining engineering practice has often been based on quite uncritical acceptance of design data largely derived from simple short termpull-out tests3,4. this approach, of necessity, ignores the stress distribution along the fixed resin anchor which can have important impli

5、cations for the resultant stress distribution in the anchored rock, and for the overall stability of the anchor. although some good theoretical analyses of stress distributions along anchorages are available5 8 there is a shortage of corroborative experimental data. the preseni paper presents a simp

6、le analysis of anchor stress distribution, and compares this with experimental data from tests on instrumented resin anchors in concrete, limestone and chalk. ordg x - 2: -c. dx a - (2) but since, provided the deformation is elastic, a x -ea6x/3x, where is the extension of the bar, equation (2) beco

7、mes: d2c_, 2 rx= . dxa e(3) if the grout annulus is thin (r - a a) then the shear stress (r.) at the steel/resin interface will be representative of the shear stress in the annulus:)2rx- (r - a) g,. (4) if the annulus is thicker (r - a a) then r, will be affected by radial changes in shear stress an

8、d it can 2. theoretical stress distributionfor the purposes of simple analysis, a steel rod grouted into a rock borehole by a filled polyester or epoxy resin grout may be regarded as an elastic anchor (moduhls of elasticity e,) surrounded by a shearable grout (modulus of rigidity g) symmetrically po

9、sitioned in a rigid socket (fig. 1). the modulus of elasticity of the rock will, in fact, be about an order of magnitude greater than the resin. if a tensile force is applied to the rod, this will be transferred to the grout, through bond or shear stresses at the rod/grout interface, causing differe

10、ntial rod extension and grout shear along the anchor. at a thin diametrical slice between x and x+ 6x (fig. 1) this transfer may be represented bya 2 fo i rocrtgrout / cr - - 27rar 6x, (1) i_ , * engineering geology laboratories, university of durham, durham, england. fig . 1. stress situation m a g

11、routcct anchor. 347 348 be shown that:z.x- i.w. farmer the transfer length is equivalent to the optimum design length for the fixed anchorage. an approximate indication of shear-stress distribution along a typical resin anchor is given in fig. 2. for typical resin/steel anchor combinations k 0.01, a

12、nd (r - a)= 0.25 a, reducing to 0.2/a, in equation (14), and r x to:oo a in r/ a gg. (5) in either case, equation (3) will by substitution take the form of a standard differential:d2x_ _ dx 2 _ 0(2x= 0 . (6) zx= o-1 exp - (0.2 x/a). (16) with the standard solution:= a exp 0(x+ b expx where0( 2 (7)3.

13、 e x p e r i m e n t a l stress disiailution = et(g - a ) 2gg 2gg or in r/ a, (8) depending on the annulus thickness. equation (7) can be solved for any given boundary conditions; in this case: (rx= ao when x= 0; (r= 0 when x= l, whence: a= ao exp -l ea exp 0(l- exp - 0(lb=ao exp e=0( exp 0(l - exp

14、- 0(l (9) (10) which gives when substituted back into equation (7):= go cosh 0(l - x) e0( sinh 0(l (ll) if l is much larger than i/0( (a likely proposition in most anchorages)then equation (11) becomes a simple exponential decay:= ea0( andzx= a0(ao exp - 0(x.ao e x p - c x (12) a series of tests wer

15、e carried out on instrumented 20 mm dia steel bars grouted into 28mm dia holes in concrete, limestone and chalk. laboratory moduli and strengths are summarised in table 1. the grouted lengths were 350 and 500 mm in-concrete, 500 m.m in limestone and 700 mm in chalk. each bar was instrumented with si

16、x or seven axially directional e.r.s, gauges equally spaced on a machined surface (fig. 3). the grout comprised a slate-dust filled epoxy resin, pre. mixed and poured into the hole before insertion of the instrumented bar. the anchor holes were drilled into freshly exposed surfaces i n the limestone

17、 and chalk, and were formed around a liner in the concrete, which was cast into a 100 mm dia steel tube in the laboratory. the holes were grout filled to the surface and the resin allowed to cure for 24 hr before testing. during testing the anchors were loaded against a surface bearing plate 300 mm

18、sq. at a force rate of 5 kn/min. surface extension was monitored continuously and strain readings monitored at 5 or 10 kn intervals. typical results are presented in figs. 4 and 5 (concrete) fig. 6 (limestone) and fig. 7 (chalk l as: (a) load-displacement curves at the grouted anchor end-not correct

19、ed for bolt extension,tw (13) if for an elastic material e is assumed equal to 2g, then 0(, equation (8), can be expressed in terms of a modular ratiok= 2g o _ eg ea ea o.q o-o4 0.o6 o-oe oi= between the shearing grout and extending rod, thus:8 k 0(2 _ or a(r - a) a2(ln r/a) k (14) f =o.i., p ( o e-

20、) j=o.i e,p (-oe x one implication of the exponential decay in equations (12) and (13) is that when 0(x is equal t o 46, exp -0(x= 0-01 andx,% are reduced to 1% of their magnitude at the top of the anchor. in other words, the load on the anchor is effectively dissipated and the anchor length is equi

21、valent to a transfer lenoth, l t given by:lt= 20 l=23ofig. 2. theoretical stress distribution along a resin anchor in a rigid socket and having a thin resin annulus. 4-6 (15) stress distribution along a resin grouted rock anchor table 1. anchor material propertiese strength 349 /m 2steel rod filled

22、expoxy resin ( 2 4 hours) 1.$o x 108 2.25 x 1c6 /m 25 x 105 6,ooo$5,000 160,ooo 33,000 13,000 3,500 (tensile) (tensile) (shear) (compressive) (compressive) (compressive) (compressive) concrete limestone chalk 2cx 106 3.(5 x 10 3 x 10 5 * regularly bedded, silt size calcite dolomite from the lower ma

23、gnesian co. durham. limestone, houghton-le-spring, * fissured fine-grained siiceous chalk from the lower chalk, chinnor, oxfordshire. (b) strain distribution curves over the anchor length, and (c) computed shear-stress distribution curves; the mean shear stress between two gauges being computed as h

24、, e= e,/a( -2)21 where 1 is the gauge separation. it is important to remember before any discussion of the results that although the shear-stress distributions represent the shear stress at the anchor-grout interface, the grout annulus in the present case is relatively thinr - a= 0-4a, see equation

25、(4). it is therefore reasonable to assume that the computed shear stress is representative of the shear stress throughout the grout, and by implication at the grout-rock interface. it is therefore reasonable to assume on the basis of equation (13) that some failure will occur in the weaker rock subs

26、trate at the grout-rock interface at higher shear stress levels. choice of the rock types and anchor lengths was based on the desire to investigate the effect of this failure on anchor reactions, and to determine the extent and type of failure. the results throughout were remarkably similar for each

27、 set of 4 chalk, 4 limestone and 4 (of each length)reo gaugec / 12g od 2500 :/80 2000 8:l g500m 4o egougei000 2 4 6 8 i0 mm gquge92 '00 500?(3n dlsplocement,)geu gouge) goug 500 400 300 distance along 200 rodx, i o0 rn m 0 i io,o0o .ooo6oo0 e 4000m 20)0 500 400 300distance along 200rod i00 x, mm

28、 0 fig. 3. instrumented anchors. fig. 4. load displacement, strain distribution, and computed shear stress distribution curves- 500ram resin anchors in concrete. top: each curve represents the strain distribution at the specified anchor load. bottom: the broken lines are theoretical shear-stress dis

29、tribution curves. the solid lines are computed from the strain distributioncurves. 350pull out failure i.w. farmeroo p u l l oul fo)lure z 80 6o gouge() 4o- l- 3c z20 -gau ge) 600 _= a:l 2000 400 :i =o 0%/ a - 1500 o i i i 2 4 6 dlsplocerne%, i 8 i0 mm o gouge/o2,/i.000 g 700 600 500distance 400alon

30、g 300rod 200x,mm io0 0 o ./ _ . . - ' u . -/ir, _.c. ii i i i i00 oo w 3ek) 300 250distance 1 1 200 along 11 150 rod | i i 0 50 8ooe x, mrn ) i0,000 25kn 2okn - 6 0 0 8000 15kni o k n 8200,- 6ooo 5kn j /74000 l 700 , 600 i 500distance 4 o0along 500 200 i00 =2000 a rod x, mm fig. 7. load displace

31、ment, strain distribution, and computed shear stress distribution curves-70omm resin anchors in chalk, 350 300 250distance 200along 150rod ioox, mm 50 c fig. 5. load displacement, strain distribution, and computed shear stress distribution curves-350mm resin anchors m concrete. top: each curve repre

32、sents the strain distribution at the specified anchor load. bottom: the broken lines are theoretical shear-stress distribution curves. the solid lines are computed from the strain distribution curves. pull oul foilure 6o io00 z 800 40 600:t 2o _1o gauqe( 400200 . 2to 500 4010 300 200 i00 d stance al

33、ong rod x, mm 1/,-,1 i so00 %, concrete anchors, and the specimen set of results in each case is entirely typical. the anchors in concrete (figs. 4 and 5) most closely simulate the assumed theoretical conditions of a rigid rock boundary, and the longer anchorsfig. 4) were arranged so that the bolt w

34、ould fail rather than the anchor. it is nevertheless interesting to note that although the experimental shear stress distribution at a pull out force of 20 kn (stress - 7 104 kn/m 2) is very close to the theoretical stress distribution, there is a substantial difference at 40 kn pull out force and t

35、his difference increases with increasing force. it is evident therefore, that at higher stresses, the whole of the fixed anchor length has debondedand that pull out resistance is largely attributable to a h level of skin friction. the non-linearity of the load-zdisplacement curve is illustrative of

36、this. in the case of the shorter anchors .in concrete (fig. 5), this pattern is repeatedat lower stress levels, but at higher stress levels, the greater movement allowed as the anchor restraint is overcome, reduced skin friction to residual levels over the top h a l f o f the anchor. dolomi theoret:

37、 betweel 1.6. it lesser d and th early st _ but a rapid reductio levels in the chalk anchors (fig. 7). it is evident that shear resistance and constraint are so low at the grout-rock interface z/2oo0i000 . ;300 disl-once along 500 400 200rod ij-'x,mm ii00 o fig. 6, load displacement, strain dist

38、ribution, and computed shear stress distribution curves-500mm resin anchors in limestone. top: each curve represents the strain distribution at the specified anchor load. bottom: the broken lines are theoretical shear-stress distribution curves. the solid lines are computed from the strain distribut

39、ioncurves. stress distribution along a resin grouted rock anchor that debonding occurs at very low stress l evels, and also that residual skin friction or shear resistance is mobilised at low pull out lorces. the implications of the results as regards the design and use of resin anchor systems are q

40、uite important. the almost universally accepted anchorpull-out formula on which design charts are based: p= 0-1srcrl (17) 351 by a. dick as part of his m.sc. advanced course m engineering geology. received 3 march 1975. references1. askey a. rock bolting with polyester resins. j. irish1 ttiohw. engrs, 18, 28 32 (197(i). 2. carr f. full hole resin anchored strata bolting in france. national coal board, prod. dept. rept. (1969). 3. franklin j. a. woodfield p. f. comparison of a polyester resin and mechanic