Chapter I 1 FRACTURING AROUND A ROCK BOLT ANCHOR. by Richard S. Culver and Tron Jorstad
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1 Chapter I 1 FRACTURING AROUND A ROCK BOLT ANCHOR by Richard S. Culver and Tron Jorstad In spite of the widespread interest in rock bolt research, relatively little is known about the critical region surrounding the bolt anchor. In analyzing the stress distribution around an opening resulting from rock bolt support, it is commonly assumed that t4he bolt is fixed at a point far enough from the surface so that the anchor does not influence the performance of the bolt. Furthermore, a bolt anchor is assumed to perform satisfactorily if it will hold the design load with a minimum amount of load relaxation, commonly called bleedoff. From the standpoint of the design engineer both of these assumptions are reasonable, but they ignore the fact that the extremely high stresses in the region of the anchor are capable of generating fractures in the rock. Lang estimated the bearing stresses for a slot and wedge anchor on a one-inch-diameter bolt to be as high as 125,000 psi. This paper describes a more thorough analysis of the magnitude of the stresses around the anchor and the nature of the potential fractures that might result. It should be emphasized that there are two types of anchor-associated fracturing which may occur. The more common form, particularly in soft rock, is severe localized crushing of the rock in the immediate vicinity of the anchor, which makes securing the anchor difficult and causes bleedoff. It is also possible to develop larger single fractures which propagate out from the anchor, affecting the strength of the entire rock mass. The formation of these larger fractures is of primary concern in this paper. In addition to estimating the contact stresses and pullout load for slot and wedge bolt anchors, Lang carried out an important study of rock bolt interaction which served as a basis for the experimental phase of this investigation. In the first phase of his tests, a plate of photoeiastic piastic was compressed by a row of piano wire bolts, simulating the interaction of bolt stress fields to form a zone of uniform compression (Fig 1). To show the supporting effect of this beam, he carried out another test series Richard S. Culver is at the Colorado School of Mines, Golden, Colo., and Tron Jorstad is in Gran, Nonvay.
2 I. Lenqth ot Bolt S- Spoc~na ot Bolts Fig. 1-Rock bolt photoelastic stress patterns. in which bolts were used to form a load-bearing beam in uncemented aggregate (Fig. 2). From the results of these tests, Lang developed several useful relations between bolt spacing, length and load which have become widely used in the design of bolting systems. Photoelastic Study EXPERIMENTAL INVESTIGATION In order to study the stress field around the anchors of a row of bolts, Q-in.-diam steel rods were anchored in the bottom of holes drilled in the edge of a 4-in.-thick plate of CR-39 photoelastic plastic. The bottom ends of the bolts were deformed and glued in the holes with epoxy cement. Each bolt was tensioned by tightening a nut on its free end and the
3 (a) Crushed rock 3 to 6 in. (b) Crushed rock 1% to 2% in. Fig. $-Rock bolt leals (after Lang). bolt load was recorded as a function of the number of degrees of rotation of the nut. When the first bolt was tensioned, a shallow, cone-shaped fracture developed at the bottom of the bolt (Fig. 3). Tensioning of successive
4 Fig. 3-Photoela.slic model-row of tensioned bolts. bolts showed that the fracture occurred quite reproducibly at a load which was later determined to be 550 lb. To eliminate the possibility of the fracture resulting from the stress concentration at the bottom of the borehole, the test was rerun with,the bottom of the borehole blocked off with paper. As in the first tests, the fracture occurred across the base of the bolt. As shown in Fig. 4, a large stress concentration developed at the tip of the crack. The cra.cks continued to propagate with increased tension in the bolt, but at no time did they give evidence of running in an uncontrolled manner. Full-Scale Bolt Test The photoelastic test series gave a useful visual picture of the stress field around the anchor and indicated the location of a probable major fracture plane, but at best it is only a qualit.ative approximation of the conditions around an actual bolt anchor. The fracture behavior of the plastic is different from that of rock; the photoelastic model gives a twodimensional representation of a three-dimensional problem, and most important, the anchoring technique used does not accurately represent the stress distribution around the common forms of bolt anchors. In order to more closely simulate field conditions, further tests were run using a standard wedge-type expansion shell anchored in Yule marble.
5 Fig. 4-Photoelastic model-cone-shaped anchor fracture, one boll tensioned. The test was designed specifically to develop the cone-shaped anchor fracture found in the photoelastic tests. The one-inch-diameter bolt was anchored at a depth of 8 in. in the marble block (13~26x26 in.) and was tensioned with a 30-ton hyraulic ram. In the first test block, a fracture occurred in a plane paraile1 to the axis of the bolt at a load of 20 tons (Fig. 5). It was apparent that this -L- ->*,*: : Fig. 6-Rock bolt test-cracks parallel to bolt ax&.
6 fracture resulted from the high lateral load exerted on the rock by the wedging action of the bolt anchor in much the same manner as rock is split using wedges. However, close examination of the marble block indicated that the rock was bedded in the plane of the fracture, so a second test was run in which the bolt was installccl perpendicular to the bedding. In this test, the rock failed perpendicular to the axis of the bolt, as had been originally anticipated, at a load of 15 tons (Fig. 6) Additional tests in larger Yule marhle block> confirnlcd the initial results In all of the tests, failure occurred catastrophically, but it is assumed that this was a result of the relatively small blocks, the short bolts, and the energy stored in the hydraulic fluid in the ram. Evidence of the anchor fracture was also found in a test program carried out at the CSM Experimental Mine for the purpose of determining the stress field around a rock bolt as well as evaluating the performance of various borehole extensometers. As illustrated schematically in Fig. 7, nine 15-ft, 13-in.-diarn bolts were installed in a 3-ft-diam bolt circle. The extensometers were mounted in boreholes inside the bolt circle so that, each one was exposed to the same stress field. For the multiple position extensometers, stations were placed at dibtances of 2.5, 5, 10, and 15 ft from the rock surface. This placed the bottonl station just below the plane of the bolt anchors. The bolts were loaded and unloaded according to a schedule designed to evaluate the response of the instruments, as well as determine the time-dependent response of the rock to the bolt load. The bolts were tensioned to a design load of 30 tons using a hydraulic ram The compressive deformation of the rock between the surface and third station at a load of 30 tons varied from in. to 0.01 in. at different points in the bolt circle, presumably because of the fractured nature of Fig. 6-Rock bolt test--conr-,\hliped truchor fmclure.
7 FRACTURE PLANE I ROCK < SIDE VIEW MULTIPLE POSITION MPBX STATION POSITIONS EXTENSOMETER-MPBX Fig. 7-Bolt circle test. 0 SINGLE POSITION EXTENSOMETER- SPBX the rock. However, the four multiple position extensometers which gave useful results all indicated a zone of tensile strain between the bottom two anchors which, it was concluded, resulted from the formation of the coneshaped anchor fractures. The extensometer borehole was in each case about one foot from the nearest bolt so the anchor fractures must have propagated at least that far. The average fracture opening for the various extensometers was estimated to be about in. This is much too large a tensile displacement to be attributed to elastic tensile strain, even if it were measured in the immediate vicinity of the rock bolt anchor. STRESSES AROUND THE BOLT ANCHOR Although both the photoelastic study and the fuli scale bolt tests gave conclusive evidence that it is possible to generate large fractures in the vicinity of a bolt anchor, field conditions are far too varied to be able to predict where or when such a fracture would occur. However, a knowledge of the magnitude and distribution of the stresses involved would help in describing the conditions which would initiate a large fracture. A mathematical model of an idealized rock bolt anchor was developed for this purpose. To select an appropriate mathematical model, it was necessary to review the common forms of rock bolt anchors. Three typical anchors are shown in Fig are based upon the wedging principle in which the bolt anchorage results from friction between the borehole and anchor, which in turn results from a large normal force developed by the wedge. The cone-type wedge develops a relatively uniform normal load around the circumference of the borehole, while the flat wedge gives a diametrically directional load. The two expansion shell anchors distribute the
8 Fig. 8-Rock bolt anchors. normal load fairly evenly along the length of the bearing surface, while the slot wedge type develops a highly concentrated load on the back edge of the anchoring surface. Slight modifications to the stress field will also result from a serrated surface such as that on the flat wedge-type expansion shell anchor. The model selected which most nearly approximates the cone-type anchor, consists of a combined uniform normal and uniform shear loading over a cylindrical bearing surface, as illustrated in Fig. 9. This is considered to be a conservative model since it avoids the stress concentrating factors resulting from serrations and nonuniform normal load. Because of the complexity of three-dimensional elasticity solutions, a modified two-dimensional solution was used to represent this type of surface load- -* -=====Y SHEAR FORCE p ( = ~ COMBINED FORCE P(xny) Fig. 9-Anchor model.
9 ing. This simplification did not seriously affect the determination of stresses near the borehole surface where the fractures would form, since the three-dimensional solution is identical to the two-dimensional at the surface and only becomes significantly different at distances greater than about 5 pct of the borehole diameter. The solution for the two-dimensional surface loading illustrated in Fig. 9 was obtained from Frocht's Ph~toelasticity.~ The modification to account for the three-dimensional stress field myas obtained by multiplying the stresses obtained for the two-dimensional solution by the factor (r,/r) 2, where r, is the radius of the borehole, and r is the distance from the axis of the borehole to the point where the stresses are being determined. This factor was obtained from the plane-strain solution for the stress around a borehole with internal pressure, P, where g, and U, are the tangential and radial stress, respectively. The equations were further modified for convenience in determining the stresses in the critical plane perpendicular to the base of tlhe anchor (represented by the X axis in Fig. 9) by introducing the dimensionless variable k=x/l, where x is the distance into the rock from the borehole in the direction of the X a,xis and L is the length of the bearing surface. The equations, thus modified, are as follows: For the shear loading, q,: For the normal loading, q,: X where 0= arctan - and t=plate thickness in 2-D solution. L
10 It can be seen from Eq. 3 that o, approaches an infinite value as k approaches zero, and it is this large tensile stress at the corner of the anchor which caused the conical fracture obtained in the experimental investigations. In order to determine the magnitude of these stresses, the following values were used from the laboratory tests, tensile load, F = 30,000 Ib anchor length, L = 2.5 in anchor diameter, D = 1.75 in. The term for the shear loading intensity, q,/t, will be equal to the tensile load divided by the shear surface area, TDL, The normal loading intensity term, q,, will depend upon the normal load required to develop the necessary shear load. In the limit, the coefficient of friction could be zero requiring an infinite stress or, as in the case of the photoelastic model, no normal load would be required to develop the necessary shear stress. More realistic values for the coefficient of friction range from 0.5 to 1.O.* Normal loads representing values of p considerably less than that required to restrain the anchor could occur in the expansion shells due to sliding on the wedge surfaces in the anchor. Because of the uncertainty in this factor, solutions were obtained for values of p equal to 0.5, 1.0 and m, the last representing the conditions in the photoelastic tests of no normal load. The numerical results are given in Table I and in Fig. 10. The solutions for the two components of the surface loading were obtained separately and then added together. The resulting stresses were used to determine the major and minor principal stresses in the X-Y plane. These are plotted in Fig. 10 as a function of the distance x from the borehole surface along with ths angle between the minor principal stress and the X axis. It can be seen that while the values of the principal stresses are strongly influenced by the value of p, the difference between the major and minor principal stress is relatively unaffected by p. Furthermore, the zero normal load (p= m) in the photoelastic tests was the optimum condition for obtaining the cone-shaped tensile fracture. One of the limitations of the two-dimensional solution used is that it does not give a value for the tangential stress around the borehole which would cause the fractures parallel to the axis of the borehole. However, referring back to Eq. 1, it can be seen that a reasonable value for this * Lang used a value of p = 0.5 in his calculations. However, this seems small in view of the observed plastic deformation of the anchor surface.
11 Table I. Stress Distribution Along X Axis u-2 Shear Loading Normal Loading 2 A, rp - in.) k U S xa TXY. "Y" uxn 7rp ' P 4 cp r o 0 0 co a 0 +d = ' ? d ' ~1 P ' i " 0 P="O " ' " z 0 0 co co 0 m d " p= " " F ' " 8
12 Fig. 10-Principal stresses for 'variozis normal loads. stress would be a,= -a,. This approximation would become accurate at the borehole surface away from the ends of the anchor. It can also be shown that anywhere except at the end of the anchor for which the values in Table I are calculated, the value of U, is twice those given in the table, so the average tangential stress under most of the anchor for the values used would be 2x1090=2180 psi. This stress would be expected to decrease according to Eq. 1 out to the distance where the finite length of the anchor begins to affect the solution. This elastic solution says nothing about the direction or extent of propagation of the anchor fractures. As soon as the fracture is initiated, it alters the stress field. Close observation of the fractures obtained in the photoelastic tests and in the Yule marble show that the angle of the fracture plane with the X axis in the mathematical model is quite close
13 to the angle Q between the minor principal stress and the X axis as shown in Fig. 10. It still cannot be stated conclusively that the fractures observed in the laboratory will occur in practice, although the stress levels appear high enough to initiate the fractures. It will depend upon external conditions whether or not the fractures will grow to a dangerous size. Nevertheless, the possibility of such fractures occurring suggests several practical measures which could be used in the field to avoid their occurrence: 1. In stratified roofs, where propagation of the cone-shaped fractures could break the entire roof "beam" loose from its hanging support, the bolt lengths should be staggered. 2. Except in special instances, bolts should not be tensioned to loads higher than those required for good contact between the plate and the surface rock. (Bolts subjected to nearby blasting are shock loaded to loads far in excess of the design value.) 3. In a vertically jointed rock, flat wedge-type anchors should be oriented so that the directional normal load is parallel to the jointing rather than perpendicular to it, thereby minimizing the chance of the wedging action of the anchor opening new or existing fractures parallel to the bolt axis. ACKNOWLEDGMENT This study was performed under the support of the American Cyanamid Company and the United States Army Corps of Engineers. REFERENCES 1. Lang, T. A.: Rock behaviour and rock bolt support in large excavations: New York, Am. Soc. Civil Eng., Oct. 1957,110 pp. 2. Frocht, M. M.: Photoelasticity: New York, John Wiley and Sons, Inc., 1948, vol. 2, pp
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