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 along 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-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 utilisation[1,2] of resin grouted rock bolts and anchors in civil and mining engineering practice has often been based on quite uncritical acceptance of design data largely derived from simple short term"pull-out" tests[3,4]. This approach, of necessity, ignores the stress distribution along the fixed resin anchor which can have important implications 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 available[5 8] there is a shortage of corroborative experimental data. The preseni paper presents a simple 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 -Ea6~x/3x, where~ is the extension of the bar, equation (2) becomes: 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 and 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 positioned 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 differential 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 by~a 2

fo I

rocRT~grout

/

~cr~ -

--

27rar~ 6x,

(1)

i_

¢"

,~

* Engineering Geology Laboratories, University of Durham, Durham, England.

Fig

. 1. Stress situation m a groutcct 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, and (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:d2~x_ _

dx 2

_

0(2~x= 0 .

(6)

zx= O-1 exp - (0.2 x/a).

(16)

with the standard solution:~= A exp 0(x+ B exp~x where0( 2

(7)3. E X P E R I M E N T A L STRESS DISI~AilUTION

= E~t(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 - 0(L

(9) (10)

which gives when substituted back into equation (7):~=

go cosh 0((L - x)

E~0(

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=½ a0(ao exp - 0(x.ao e x p - c~ x

(12)

A series of tests were 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 six 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 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 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 corrected 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