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The function of roof bolts and a new device for underground roof stabilisation Karara, Said Mahmoud 1969

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THE FUNCTION OF ROOF BOLTS AND A. NEW DEVICE FOR UNDERGROUND ROOF STABILISATION by SAID MAHMOUD KARARA B . S c , C a i r o U n i v e r s i t y , 1951 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n the Department', o f MINERAL ENGINEERING » We a c c e p t t h i s t h e s i s as conforming to the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA In presenting this thesis in part i a l fulfilment of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library shall make i t freely available for reference and study. I further agree tha permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Depa rtment The University of B r i t i s h Columbia Vancouver 8, Canada Date I n v e s t i g a t i o n s were c a r r i e d out to reach a compre-hensive understanding of the a c t i o n of the roof "bolt t o -gether with, i t s anchor, on the rock, and how t h i s a c t i o n helps i n s t a b i l i s i n g the r o o f i n underground openings. Tests were' conducted on a two, dimensional, p h o t o e l a s t i c epoxy model, as w e l l as on a limestone rock model. Results and t h e i r a n a l y s i s revealed t h a t , with the present design of the roof b o l t , the most e f f e c t i v e type of anchor i s the one w i t h the lowest-transverse f o r c e . Thus, the glue-anchored h o l t s are more e f f e c t i v e than the expansion s h e l l anchored ones. I t was found that the expansion-shell-anchored b o l t s give high l a t e r a l compressive s t r e s s e s around the anchor, l o n g i t u d i n a l compressive s t r e s s e s along t h e . e f f e c t i v e l e n g t h of the b o l t , and t e n s i l e l a t e r a l s t r e s s e s i n be-tween the end b e a r i n g plates.. The epoxy anchored standard b o l t s give no s i g n i f i c a n t transverse'compressive stresses around the anchors,' nor between .them, . l o n g i t u d i n a l compressive s t r e s s e s along the e f f e c t i v e l e n g t h of the b o l t , and • l a t e r a l t e n s i l e s t r e s s e s inbetween the end bearing p l a t e s . In p r a c t i c a l a p p l i c a t i o n , the l i m i t a t i o n s imposed by present rock b o l t designs i n h i b i t the attainment of s t r e s s d i s t r i b u t i o n patterns i n accord w i t h t h e o r e t i c a l roof s t a b i l i s a t i o n p r i n c i p l e s . To increase the bolt e f f i c i e n c y i n s t a b i l i s i n g the r o o f s , a compressive device was found very u s e f u l i n adding l a t e r a l compression to the surrounding s t r e s s f i e l d . This device can be used alone or f i t t e d to rock b o l t s - i i i to induce compressive l a t e r a l stresses i n zones where such stresses might help to form a stable.'1.roof. - i v -TABLE OF CONTENTS T i t l e i A b s t r a c t i i Tab le o f con ten t s i v L i s t o f f i g u r e s v Acknowledgement v i i I n t r o d u c t i o n . . 1 D e s i g n o f the exper iments 3 Model d e s c r i p t i o n 4 Procedure and r e s u l t s o f the f i r s t group o f t e s t s 12 Discussion o f r e s u l t s f o r the f i r s t group o f t e s t s 2 3 P rocedure and r e s u l t s o f the second group of t e s t s 29 D i s c u s s i o n s and c o n c l u s i o n s of the second group o f t e s t s • 34 P o s s i b l e a p p l i c a t i o n s 42 A p p l i c a t i o n o f Mohr theory o f f a i l u r e to mine r o o f s 45 C o n c l u s i o n s 48 Suggestions f o r f u r t h e r work 49 Re fe rences " 50 Appendix No I C a l i b r a t i o n o f p l a s t i c m a t e r i a l s 51 Append ix No II Model r o c k p r o p e r t i e s 53 Append ix No I I I Rock m a t e r i a l r e s i d u a l s t r e s s e s 55 Append ix No IV Sample c a l c u l a t i o n 57 Append ix No V E r r o r s 58 - V -LIST OF FIGURES —I———•! • llll — 1- Roof bolts used i n p l a s t i c model. 6 page 2- The design of the p l a s t i c model. 7 3- The design of the o p t i c a l assembly 9 4- Rock model i n 45° oblique incidence position.11 5- 0° i s o c l i n i c s , p l a s t i c model, expansion s h e l l anchored b o l t s . 14 1G- Di t t o , with glue anchored b o l t s . 20 6- Normal incidence isochromatics, p l a s t i c model, expansion s h e l l anchored b o l t s . 15 8- D i t t o , without bolt p u l l . 18 11- D i t t o , with glue anchored b o l t s . 21 7- L a t e r a l and l o n g i t u d i n a l stress d i s t r i b u t i o n between two expansion s h e l l anchored b o l t s . 16 9- D i t t o , without bolt p u l l . 19 12- D i t t o , with glue anchored b o l t s . 22 13- Normal incidence isochromatics, rock model, expansion s h e l l anchored bolts, 12" spacing at 6 tons load. 24 20- D i t t o , with lower compressive device. 37 18- 45° oblique incidence isochromatics, rock model, epoxy anchored bolts with lower compressive device. 35 14- L a t e r a l and l o n g i t u d i n a l stress d i s t r i b u t i o n between two expansion s h e l l anchored bolts, rock model, 6tons load, 12" spacing. 25 19- Di t t o , between epoxy anchored bolts,with lower compressive device, 10 tons load, 24" spacing. 36 21- D i t t o , f o r expansion s h e l l anchored bolts, with lower compressive device, 6 tons load, 12" spacing. 38 17- Lower compressive device. 33 22- Possible tangential stress d i s t r i b u t i o n due to the expansion s h e l l anchor. 40 - v i -23- Effect of different bolt designs on simple beam roof. 44 24- Mohr c i r c l e . 46 25 Calibration chart for the plastic materials. 52 26- Relaxation test f i e l d stress directions. 57 27- Srror due to oblique incidence reading i n f l a t and steep fringe gradients. 60 v i i ACKNOWLEDGMENT I wish to express my g r a t i t u d e and a p p r e c i a t i o n to Dr. C. L. Emery, the p r o j e c t s u p e r v i s o r , f o r h i s continuous guidance and encouragement. I am g r a t e f u l to Dr. Duncan, the Head o f the Mecha-n i c a l Department, f o r h i s s i n c e r e h e l p and g e n e r o s i t y w i t h h i s time and equipment. I wish to express my thanks to P r o f e s s o r Crouch and Dr. I. Bain, f o r t h e i r u s e f u l d i s c u s s i o n s and c r i t i c i s m . Thanks to a l l the members o f the M i n e r a l E n g i n e e r i n g Department and the graduate students f o r t h e i r h e l p f u l s u g g e s t i o n s . P a r t i c u l a r thanks to Mr. R. Bays who showed g r e a t s k i l l i n manu f a c t u r i n g the p r e c i s i o n model p a r t s . I am i n d e b t e d to the G i a n t Y e l l o w k n i f e Mines L t d . , and the N a t i o n a l Research C o u n c i l o f Canada f o r t h e i r f i n a n c i a l support without which t h i s study would have not been p o s s i b l e . INTRODUCTION Roof bolts i n d i f f e r e n t forms and materials have been used f o r s t a b i l i s i n g the roofs i n many mines. Wooden, bronze and i r o n bars have been used. Ancient Egyptians and Chinese used the wooden dowels to l i m i t the l a t e r a l movement of fractured rocks. The use of stressed s t e e l roof b o l t s as roof supports, started i n the P o l i s h and German c o a l f i e l d s . They have been used i n the S i l e s i a n and Ruhr v a l l e y coal mines f o r more than 1 0 0 years. Roof bolts are gradually replacing the older types of support as they are superior i n many ways; they are econo-mical to purchase, and easier to transport and to i n s t a l l ; they do not occupy any of the working area and hence the excavations can be minimised. Bolts are not subjected to a l l the hazards of b l a s t i n g and of being knocked down by heavy machinery. However, the use of bolts i n underground roofs was not widely accepted i n the United States u n t i l World War I I . Since then, f a t a l i t i e s from roof f a l l s have been reduced by 5 0 % . In 1968, approximately 75 m i l l i o n bolts of 6' ave-rage length were used i n the United States underground mines. Out of that number, 65 m i l l i o n were used i n coal mines. The same r a t i o holds approximately f o r the roof bolts used i n underground mines throughout the world. By using roof bolts extensively i n coal mines, where s t r a t i f i e d roofs are predominant, rather than i n metal mines where fractured roofs are most common, i t shows - p r a c t i c a l l y , that the roof bolts with t h e i r present design, are not as good f o r s t a b i l i s i n g fractured roofs as they are f o r b u l l -- 2 -ding up m o n o l i t h i c beams i n s t r a t i f i e d rocks. 1 7 4-3 6 I n v e s t i g a t o r s such as Lang ' , Panek,' ,and Parsons have con t r i b u t e d valuable i n f o r m a t i o n to t h i s s u b j e c t . Yet, the f u n c t i o n of the roof b o l t together w i t h i t s anchor i n s t a b i l i s i n g rock s t r u c t u r e s i s not completely understood. The scope of t h i s work i s to i n v e s t i g a t e the f u n c t i o n of the roof b o l t w i t h the d i f f e r e n t types of anchor, on underground r o o f s , o f f e r i n g suggestions f o r any improvement found s u i t a b l e . The i n v e s t i g a t i o n of the roof b o l t a c t i o n , comprises the i d e n t i f i c a t i o n of the p a r t i c u l a r c o n t r i b u t i o n by every main part of the r o o f b o l t to the over a l l s t r e s s f i e l d r e s u l t i n g from b o l t i n g . Also, comparison between the d i f f e r e n t s t r e s s f i e l d s caused by the d i f f e r e n t types of anchor, i s necessary to e s t a b l i s h a c r i t e r i o n f o r the proper choice of an anchor f o r a s p e c i f i c case. - 3 -THE EXPERIMENTAL WORK 1- Design of The Experiments The work was based on model experimentation. A photoelastic p l a s t i c model was used to predict the be-haviour of the roof bolts together with t h e i r anchors, and to get o r i e n t i n g and co-ordinating r e s u l t s . A rock model was designed to check the a p p l i c a b i l i t y of the r e s u l t s obtained from the photoelastic model i n rocks, using f u l l s i z e bolts and anchors. The scheduling of the experiments f a l l under two main groups. 1-1 The F i r s t Group of Tests: 1-1-a The Photoelastic P l a s t i c Model; To compare the e f f e c t of the two main types of anchor i e the expansive and the glued ones on the action of loaded roof bolts on the surrounding rock, two experiments were designed using; 1—1 —a—1 A standard expansion-shell-anchored b o l t . 1-1-a-2 A standard epoxy-anchored b o l t . 1-1_a-3 A t h i r d experiment was designed to investigate the p o s s i b i l i t y of using the expansion s h e l l alone as compressive device, A standard expansion-shell anchor was used and the bolt tension was released a f t e r loading the anchor. 1-1-b The Rock Model; At t h i s stage, a sing l e experiment was designed to investigate the e f f e c t of the standard expansion s h e l l -anchored bolt i n the rock model. - 4 -1-2 The Second Group o f T e s t s The conduct o f these t e s t s depended on o b t a i n i n g f a v o r u a b l e r e s u l t s from the f i r s t group o f t e s t s . 1-2-a The P h o t o e l a s t i c Model; To t e s t the e f f e c t o f the b o l t s anchored with the anchor type which proved ( b y the 1st group o f t e s t s ) to be the most s u i t a b l e f o r the r o o f s t a b i l i s a t i o n , t o -g e t h e r w i t h any m o d i f i c a t i o n s which might be found s u i t -a b l e to i n c r e a s e the a c t i o n o f the b o l t i n such s t a b i l i -s a t i o n . 1-2-b The Rock Model; The experiments were designed to be conducted on the r o c k model u s i n g expansion s h e l l and epoxy anchored b o l t s and u t i l i s i n g any m o d i f i c a t i o n s which might prove to be p r o m i s i n g i n the p l a s t i c model t e s t s . As the 1st and 2nd group o f r o c k model experiments were c a r r i e d out on the same model, and guided by the r e s u l t s o b t a i n e d from the p h o t o e l a s t i c model, the rock model experiments were c a r r i e d out i n the f o l l o w i n g o r d e r ; 1- Epoxy-anchored b o l t s spaced a t 24" w i t h lower compre-s s i v e d e v i c e . 2- Standard expansion s h e l l - a n c h o r e d b o l t s spaced a t 12". 3- Expansion s h e l l - a n c h o r e d b o l t s w i t h lower compressive d e v i c e spaced a t 12". 2- Model D e s c r i p t i o n 2-1 The P l a s t i c Model: A f t e r comparing between d i f f e r e n t p h o t o e l a s t i c model methods, i t was concluded t h a t s u f f i c i e n t d a t a can be obtained by using a two dimensional p l a s t i c model. To simulate the a c t i o n of the expansion s h e l l , a small model of t h i s anchor was made. This however, l i m i t e d us to a scale 1/3 as a precise model of the expansion s h e l l i s very d i f f i c u l t to manufacture i f the scale i s any smaller, i n which case we might end with e r r a t i c r e s u l t s . Bolts 24" long,1/4" 0 were used with 8" centers spa-cing. To simulate the constraining tangential t e n s i l e stresses due to the rock surrounding the d r i l l - h o l e s , and to carry the stresses through out the model, two p l a s t i c sheets of 1/4" thickness were glued together with a r e f -l e c t i v e glue. The upper sheet has s l o t s of 2C4-" x £" spaced at 8" centers, to simulate the d r i l l - h o l e s . Figure No 1 shows an exploded view f o r the roof b o l t and the expansion s h e l l model used. Figure No 2 shows the design of the two dimensional p l a s t i c model. An arrangement l i k e t h i s gives a c l e a r idea about the state of stress due to the roof bolt together with the anchor i n the plane containing the bo l t s center l i n e s . A s e n s i t i v e photoelastic p l a s t i c sheet, ( P.S.M. 5 epoxy ) of 1/4" thickness was used. I t s c h a r a c t e r i s t i c s are as follows: The above c h a r a c t e r i s t i c s were supplied by the manufacturer. A c a l i b r a t i o n t e s t was ca r r i e d out on a 2" 0 c i r c u l a r disk gave the same stress fringe value. For the c a l i b r a t i o n test procedure and r e s u l t s , please r e f e r to Apprendix No I. Stress fringe value Modulus of e l a s t i c i t y Poisson's r a t i o = 60 p s i . i n / f r i n g e = 450,000 p s i = 0.36 F i g u r e No 1-Roof B o l t s Used In P l a s t i c Model, a - Expansion s h e l l anchored b o l t . b - Glue anchored b o l t w i t h lower comp. d e v i c e . 1 - Expansion s h e l l l e a v e s . 2 - Expansion s h e l l wedge. 3 - Anchor to be glued. 4 - Lower compressive d e v i c e . 5 _ 1/4" 0 b o l t . 6 - End bear i n g p l a t e . 7 - E l e c t r i c l o a d c e l l . 8 - S t e e l Washer. 9 - Ti g h t e n i n g nut. 4 ' — 11 / 1 t F i g u r e No ' „2 The Des ign o f The P l a s t i c Model - 8 -During the work i t was found that t h i s epoxy sheet exhibits very low creep and time edge e f f e c t . Small r e s i -dual stresses were detected during the work. As the work on the p l a s t i c model i s q u a l i t a t i v e r a t -her than quantitative, random loading was used, and as i t was expected, the stress patterns were consistently p a r a l l e l i n a l l ceses. E l e c t r i c s t r a i n gauges load c e l l s f i x e d to the bolts between the nut and the end plate, made i t pos-s i b l e to measure the loads on the bolts and keep them symmetrical. No external stresses were applied, only end r e s t r a i -ning was used. Due to the large area of the model (24" x 24"), a sp e c i a l l i g h t s t e e l structure was erected to hold the l i g h t source, the lenses, and the camera. A pin-head white l i g h t source, two 12" 0 c o l l i m a t i n g lenses of 60" f o c a l length and a 35 mm camera with a telephoto lens and a 80 ASA Kodacolor f i l m were used f o r photographing the i s o c l i n i c s and the isochromatics. Figure No 3 shows the o p t i c a l assem-bly . To i s o l a t e the p r i n c i p a l stresses, the oblique method with a 45° i n c l i n a t i o n was used. To minimise the errors due to the l i g h t r e f r a c t i o n while passing obliquely from the a i r into and from the epoxy, a 12" x 9" prism was made out of 1/8" thick p l e x i g l a s s sheets and f i l l e d with colou-r l e s s p a r a f f i n o i l . Both the pl e x i g l a s s and the p a r a f f i n o i l have a r e f r a c t i o n index of 1.42. When used, a t h i n p a r a f f i n o i l l a y e r was used as a l i g h t path medium between the prism and the epoxy. To allow precise measuring of the stresses at d i f f e r e n t points, a precise retarding analyser which reads to 0.01 of a fr i n g e was used i n both normal and - 9 -F i g u r e No 5 The Design of The O p t i c a l Assembly f o r  4 5 ° Oblique Incidence - 10 -oblique incidence methods to locate the fri n g e order. 2-2 The Rock Model; A 24" x 3 6 " x 6 " l o c a l Haddington b u i l d i n g lime.stone slab was used as the rock model. Bedding planes were p a r a l -l e l to the 3 6 " x 6 " faces. Holes 18" long and 1 1/8" 0 were diamond d r i l l e d i n the middle of the 6" . thickness and normal to the 3 6 " faces. To simulate the constraining action of the peripheral rocks, a \" thick s t e e l box was welded around the rock. The space between the rock and the box was then f i l l e d with epoxy cement of compressive strength of 18 , 0 0 0 p s i . Five \ n 0 high t e n s i l e strength s t e e l bolts with p l a s -t i c s t r e s s meters were f i x e d across the box surfaces to keep i t from deformation i f the rock deforms. Two methods of s t r a i n measuring were used; s t r a i n gauges and photoelastic coating. As we need only the s t r e -sses along and normal to the l i n e of symmetry between the two bolts, 9 0 ° s t r a i n gauge rosettes were embedded 3" deep along the l i n e with t h e i r i n d i v i d u a l gauges aligned along and normal to i t . This arrangement allows d i r e c t readings of ( C x + v 6 Y ) and ( C y + v 0 X ) from which and cry. are calculated using the formulae; B ( e "+ v e ) °y 1 _ v 2 x ~y ' * ~x Budd s t r a i n i n d i c a t o r of 2 u"/in s e n s i t i v i t y was used to-gether with a Budd s t r a i n gauge switch box. To avoid stress concentration around the s t r a i n gauge hole ends, these holes were f i l l e d with a c r y l i c cement having Figure No 4 Rock Model i n 4 5 ° Oblique Incidence P o s i t i o n . 1 - Rock slab i n the constraining box. 2 - Roof bolts with photoelastic stressmeters. 3 - Box s t r a i n i n g rods with stressmeters. 4 - P l a s t i n g coating on the rock surface. 5 - 12" 4 5 ° prism. 6 - 12" 0 c o l l i m a t i o n lenses. 7 - Budd s t r a i n gauges switch box. 8 - Budd s t r a i n i n d i c a t o r . 9 - The housing s t e e l frame. - 12 -almost the same strength, E and v as the rock. The epoxy coating sheet was cast with a 1/4" t h i c k -ness from Hysol r e s i n No 2 0 5 3 and hardener No 3527, at a r e s i n / hardener r a t i o of 3 / 1. I t has a stress f r i n g e f a c t o r of 5 6 p s i . i n / f r i n g e , modulus of e l a s t i c i t y 450,000 p s i and a Poisson's r a t i o of 0.35. I t was glued with a r e f l e c t i v e cement to the middle 12" x 24" on one of the 3 6 " x 24" faces of the rock which was l e f t without cons-t r a i n i n g . Figure No 4 shows the rock model assembly. For the c a l i b r a t i o n t e s t of the epoxy please r e f e r to Appendix No I. The rock has a compressive strength of 1 3 , 5 0 0 p s i and t e n s i l e strength of 1020 p s i . The average modulus of e l a s -t i c i t y E along and normal to the l i n e of symmetry i s 4.1 x 10^ p s i and the average v i s 0.28. Procedure and r e s u l t s of such tests are given i n Apprendix No I I . A r e l a x a t i o n t e s t was c a r r i e d out on an oriented 2" cube of the model rock. I t was found that the r e s i d u a l stresses i n the rock are comparatively small and could not be determined with the a v a i l a b l e equipment. However, the f i e l d thrust vector d i r e c t i o n was located. I t l i e s along the bedding planes and dips about 60 to the model surface. Appendix No I I I shows the t e s t and i t s r e s u l t s . The o p t i c a l assembly i s the same used with the p l a s t i c model. 3- Procedure and Results of The 1st Group of Tests  3-1 The Photoelastic Model; The two main types of anchors now i n use i e the expansion and glued ones are tested. As the stresses induced - 13 -by the holt assembly i n the roof at the l i n e of symmetry between two consecutive bolts are the minimum, then they are the e f f e c t i v e ones. For t h i s reason, only the stresses along and normal to the l i n e of symmetry between the bolts were measured. To reduce the abscissa values f o r c l a r i t y of comparison, only the pattern of the l a t e r a l and l o n g i -t u d i n a l stress d i s t r i b u t i o n along and normal to t h i s l i n e were shown. Curves trace n^ and n^ which are the photoelas-t i c measurments of retardation due to these stresses. To get the stress i n p s i at any point simply multiply e i t h e r n.j or n 2 times 120, (-^ "^  • 3-1-1 The bo l t with expansion s h e l l ; The expansion s h e l l wedges were introduced i n place and the bolts were strained. Using plane polarised white l i g h t , the i s O c l i n i c s were pho-tographed. Figure l o 5 shows the i s o c l i n i c s at 0°. This shows that when the loads on the two consecutive b o l t s are equal, the d i r e c t i o n of the p r i n c i p a l stresses i s e i t h e r along or normal to the l i n e of symmetry between the bolts, which i s not the case f o r unequal loading. Therefore, a l l the experiments were done with equal loading, using e l e c t r i -c a l s t r a i n gauge load c e l l s to detect the load. This made i t possible to use large scale oblique incidence to sepa-rate the p r i n c i p a l stresses with one r o t a t i o n . Using c i r c u l a r l y polorised normal incident white l i g h t , the isochromatics were photographed, and located at d i f f e r e n t points on the l i n e of symmetry* Figure Nc 6 shows the normal incidence isochromatics. With the 45° oblique incidence set up, the f r i n g e order at the same points were located. F i g u r e No 5~ 0 ° I s o c l i n i c s . P l a s t i c Model, Expansion  S h e l l Anchored B o l t s . 1 - The r i g h t panel symmetrically loaded. 2 - The l e f t panel randomly loaded. ft Figure No ' 6 Normal Incidence Isochromatics, P l a s t i c Model, Expansion S h e l l Anchored Bolts - 16 -+. is +'o +o.f 0 _o.s- _ i.o _/.$• _s,o -J.S -3-0 F i g u r e No 7 L a t e r a l and L o n g i t u d i n a l S t r e s s D i s t r i b u t i o n  Between Two Expans ion S h e l l Anchored B o l t s i n  P l a s t i c Model ( P a t t e r n o f ) - 17 -Prom the f r i n g e o r d e r o f the d i f f e r e n t p o i n t s a t the normal and o b l i q u e i n c i d e n c e , the magnitudes o f the i n d i v i d u a l p r i n c i p a l s t r e s s e s were c a l c u l a t e d u s i n g the f o l l o w i n g formulae: a1 = " I t (/2 n d " n n } = f t n 1 a2 = "It. ( / 2 n o 2 ; + n n ) = f t n 2 where, f = s t r e s s f r i n g e v a l u e o f the p l a s t i c , p s i . i n / f r i n g e * t = t h i c k n e s s o f the model, i n . no1 * n o 2 = f r ^ n & e o r d e r i n o b l i q u e i n c i d e n c e i n d e c i m a l s . n n = f r i n g e o r d e r i n normal i n c i d e n c e i n d e c i m a l s . F i g u r e No 7 shows the p a t t e r n o f the l a t e r a l and l o n g i -t u d i n a l s t r e s s d i s t r i b u t i o n (n^ and n£) a l o n g and normal to the l i n e o f symmetry. 3-1-2 Loaded expansion s h e l l without b o l t p u l l : With the expansion s h e l l loaded i n p l a c e , the b o l t s were r e l e a s e d from t e n s i o n . The i s o c l i n i c s as w e l l as the normal and o b l i q u e i n c i d e n c e i s o c h r o m a t i c s were photographed and r e -corded and the s t r e s s e s were c a l c u l a t e d as shown above. F i g u r e No 8 shows the normal i n c i d e n c e i s o c r o m a t i c s . F i g u r e No 9 shows the p a t t e r n o f the l a t e r a l and l o n g i t u -d i n a l s t r e s s d i s t r i b u t i o n a l o n g and normal to the l i n e o f symmetry. 3-1-5 Glue anchored b o l t s : The upper end o f the b o l t s were glued to the model and the t e n s i o n was a p p l i e d to the b o l t s u s i n g b e a r i n g p l a t e s and n u t s . I s o c l i n i c s , normal and 18 . , _ . F i g u r e No 8 Normal Incidence Isochromatics, P l a s t i c  Model, Expansion S h e l l Without B o l t P u l l - 1 9 -* \ * V 22 L0N6IT0DINHL -• — 1 \ 10 1 ' 18 A 1 6 1 A' . -*r, • 2 COMPRESSION + I S t ' - 6 + 0 . 5 0 -OS -i-o -US .2-0 _is _3.o F i g u r e No 9 P a t t e r n o f L a t e r a l and L o n g i t u d i n a l S t r e s s D i s t r i b u t i o n Between Two Expansion S h e l l s Without B o l t T e nsion i n P l a s t i c Model _ £ 0 _ F i g u r e No 10.-. 0 ° I s o c l i n i c s , P l a s t i c rlodel. Glue Anchored  B o l t s . Figure No 11 Normal Incidence Isochromatics , P l a s t i c  Model,•Glue Anchored B o l t s . - 2 2 -i4 1 \ ^ — L.Ofi6lTUOINFIl-\ / or-1 lf 1 / & Y -( * -. J — - ; v . * + /-y + i-o * os c - o-5 - l-o - IS -Z*> F i g u r e Ko 12 P a t t e r n o f L a t e r a l and L o n g i t u d i n a l S t r e s s D i s t r i b u t i o n Between Two Glue Anchored B o l t s In P l a s t i c Model - 23 -oblique incidence isochromatics were photographed and recorded and the stresses were calculated as shown above. Figure No 10 shows the 0° i s o c l i n i c s . Figure No 11 shows the normal incidence isochromatics. Figure No 12 shows the pattern of the l a t e r a l and l o n g i t u d i a n l stress d i s t r i b u t i o n along the l i n e of symmetry between two consecutive b o l t s . 3- 2 The Rock Model This test was conducted using two standard expansion shell-anchored b o l t s loaded at 6 tons each at a spacing of 12". I s o c l i n i c s normal and oblique incidence isochromatics were recorded and the stresses were calculated as follows, 1 x G1 p ° "TFt n i a n d G2 p = T F t n 2 As s t r a i n s i n the p l a s t i c are the same as i n the rock, then, , °i p - 61P E r / :t 1 + V and, ^2 r = G2p E r / ( 1 + v r ) The s t r a i n gauge readings were recorded and the stresses were calculated. Figure No 13 shows the normal incidence isochromatics. Figure No 14 shows the l a t e r a l and l o n g i t u d i n a l stress d i s t r i b u t i o n along and normal to the l i n e of symmetry. 4- Discussion of Results f o r The F i r s t Group of Tests 4-1 P l a s t i c Model; By examining the atreas d i s t r i b u t i o n due to the ex-pansion shell-anchored bolts, i n Figure No 7, we f i n d the - 24 -CCD SSSSSSSfc OamprttfioH 0 Tin fiOK 8 o x ', Stun I 0f«ch»/iV ' HtSvlhtnl- Force" F.«W S'rtn £~xp. Shtll •. Lckltra! torCH .: i f . S e c t i o n A - A Figure No 15 Normal Incidence Isochromatics, Rock Model  Expansion S h e l l Anchored B o l t s , 12" Spacing  6 Tons Load. lower sketch shows p o s s i b l e arrangement of fo r c e s causing asymmetric p a t t e r n shown above - 25-Fjgure No %£ L a t e r a l and L o n g i t u d i n a l S t r e s s D i s t r i b u t i o n  Between Two Expansion' S h e l l Anchored B o l t s  In Rock Model t 6 Tons Load,12" Spacing - 26 -following; 1- They give almost uniformly d i s t r i b u t e d l o n g i t u d i n a l compression on a zone about 2 / 3 rds of the bolt length (including the anchor). 2- They give a very high l a t e r a l compression i n the zone between the expansion s h e l l s . 3- They give r e l a t i v e l y high l a t e r a l tension i n the lower section of the model as well as va r i a b l e l a t e r a l t e n s i l e stresses i n the zone between those discussed above. From Figure No 9, the d i s t r i b u t i o n of the high com-pressive l a t e r a l stresses due to the expansion s h e l l anchor alone can be cl o s e l y inspected. Adding the stresses due to the bolt load, they do not reduce the anchor l a t e r a l com-pression, but reduce the l o n g i t u d i n a l tension, thus showing lower fringe order, Figure No6 and No 8 . Also, from these two figures i t i s noticable that without the bolt tension, the e f f e c t of the expansion s h e l l covers a wider area almost 1.5 times the width with the bolt tension. This shows that the expansion s h e l l or any suitable expan-sive device can be used alone as a compressive element. Examining Figure No 1 2 which shows the stress d i s t r i -bution i n case of the glue anchored bolts, we f i n d the following; 1- They give a l o n g i t u d i n a l compressive stress on a zone of about 3 / 4 the bolt length (including the anchor). 2- They give l o n g i t u d i n a l t e n s i l e stresses i n the zone above the anchor. 3 - They give v a r i a b l e l a t e r a l t e n s i l e stresses a l l over the bolt length. - 27 -From F i g u r e No 11 i t i s n o t i c e d t h a t the f r i c t i o n a l s t r e s s e s around the anchor are c o m p a r a t i v e l y s m a l l and the compressive s t r e s s e s j u s t below i t are c o m p a r a t i v e l y h i g h f o r m i n g some s o r t o f b e a r i n g shoulder, which shows t h a t t h i s type o f anchor depends mai n l y on the compressive s t r e n g t h o f the r o c k as w e l l as o f the g l u e . T h i s r e n d e r s i t u s e f u l i n s o f t rocks, s p e c i a l l y because the l e n g t h o f the anchor can be i n c r e a s e d to a l a r g e extent, hence reduce the f r i c t i o n s t r e s s e s a p p l i e d to the d r i l l - h o l e w a l l . 4-2 Rock Model: The a c t i o n o f the expansion s h e l l anchored b o l t can be shown c l e a r l y i n F i g u r e No 13, where the h i g h compre-s s i v e s t r e s s e s o f the expansion s h e l l f o r c e d the r o c k and bent the s u r f a c e upwards i n the r i g h t hand s i d e o f the un-c o n s t r a i n e d a r e a as can be c l e a r l y n o t i c e d from i n s p e c t i n g the s t r e s s p a t t e r n . U n f o r t u n a t e l y , a l t h o u g h the b o l t s and t h e i r anchors were p l a c e d and loaded s y m m e t r i c a l l y , y e t the shear s t r e s s p a t t e r n shown on the p h o t o e l a s t i c c o a t i n g i s asymmetric. I t i s c l e a r l y n o t i c a b l e from F i g u r e No 13 t h a t the anchor on the r i g h t hand s i d e has much more e f f e c t than t h a t on the l e f t hand s i d e . The same e f f e c t can a l s o be n o t i c e d i n F i g u r e No 20 where a lower compressive d e v i c e was f i x e d to the lower p a r t o f both b o l t s . T h i s asymmetric d i s t r i b u -t i o n o f s t r e s s e s may have the f o l l o w i n g p o s s i b l e e x p l a n a -t i o n s : 1- The e x i s t i n g r e s i d u a l s t r e s s e s i n the r o c k . 2- The d i r e c t i o n a l p r o p e r t i e s o f the r o c k . 3- The p o s s i b i l i t y o f asymmetric bending i n the rock under - 28 -the b o l t tension. 4- The p o s s i b i l i t y of an asymmetric e f f e c t of the constraining box. However, the shear stress pattern i n Figure No 13 and the stress d i s t r i b u t i o n shown i n Figure No 14 appear to give clear representation of the e f f e c t of the expan-sion s h e l l anchor-on the rock model. Due to the high r a d i a l compressive force of the expan-sion s h e l l anchors, and to the presence of weakness planes normal to the bolts, the rock inbetween the two anchors could not sustain the t e n s i l e normal stresses ( p a r a l l e l to the bolt d i r e c t i o n ) and a crack started along one of the weak planes, as shown by the high concentration of the f r i n g e s i n the narrow shoot. While t h i s destruction was taking place around the anchor, no s i g n i f i c a n t stress was detected i n the model along the d i r e c t i o n of the b o l t s as shown i n Figure No 14» and no t e n s i l e stress was observed between the end p l a t e s . This i s due to three f a c t o r s ; 1- The deviation of the rock behaviour from the e l a s t i c m aterial such as the photoelastic model. 2- The e f f e c t of the constraining box i n eliminating the t e n s i l e stresses which might have occured between the bearing plates i f the box was not there. 3- The bolt lengths were short compared with the spacing between them. With the increase of the length/spacing r a t i o , we would expect an increase of the l o n g i t u d i n a l compressive stresses along the l i n e of symmetry. - 29 -4-5 General C o n c l u s i o n s from The F i r s t Group o f T e s t s * 1- F o r a medium s t r e n g t h r o c k the glue anchor i s more e f f e c t i v e than the standard expansion s h e l l . 2- The d i s t r i b u t i o n o f s t r e s s e s due t o the glue anchored b o l t s i s more f a v o u r a b l e f o r r o o f s t a b i l i s a t i o n than the expansion s h e l l anchored b o l t . 3- The d i s t r i b u t i o n o f the s t r e s s e s due to the expansion s h e l l anchor alone causes i t to f u n c t i o n as a compressive element. 4- Due to the standard s t r a i n i n g assembly and b o l t t e n s i o n , a t e n s i l e zone i s cr e a t e d between the p l a t e s . T h i s t e n s i o n reduces the s t a b i l i t y o f the rock i n t h i s zone. 5- The d i r e c t i o n a l p r o p e r t i e s o f the r o c k should be taken i n t o c o n s i d e r a t i o n when d e s i g n i n g a r o o f b o l t i n g system. Based on the f o r e g o i n g c o n c l u s i o n s i t was d e c i d e d t o d e s i g n a compressive d e v i c e to be used e i t h e r a lone o r f i x e d to the b o l t , and to conduct 3 more experiments. 1- Glue-anchored b o l t w i t h the compressive d e v i c e r e p l a -c i n g the lower s t r a i n i n g assembly on the p l a s t i c model. 2- The same experiment on the rock model. 3- A t h i r d experiment u s i n g expansion s h e l l - a n c h o r e d b o l t s f i t t e d w i t h these compressive d e v i c e s r e p l a c i n g the lower s t r a i n i n g assembly. 5 - Procedure and R e s u l t s o f The Second Group o f T e s t s 5-1 Glue-anchored b o l t with lower compressive d e v i c e ' i n  the p l a s t i c model: A s p e c i a l f i x t u r e was designed to s i m u l a t e the comp-- 3 0 -r e s s i v e device around the lower end of the glue-anchored b o l t . Figure No 1-b shows an exploded view f o r t h i s arran-gement. The f i x t u r e was f i t t e d to the bolt, the assembly-was loaded, and i s o c l i n i c s , normal and oblique isochroma-t i c s were photographed and recorded and the stresses along and normal to the l i n e of symmetry were calculated as shown above. Figure No 15 shows the normal incidence isochromatics. Figure No 16 shows the stress d i s t r i b u t i o n along and normal to the l i n e of symmetry between two consecutive b o l t s . 5-2 Glue-anchored bolt with lower compressive device  on the rock model: Two 24" long, 5/8 0 bolts, of high t e n s i l e strength s t e e l were glued by epoxy cement to the upper 5" of two 24" spaced 18" long and 1.2" 0 d r i l l holes. Figure No 17 shows an exploded view of the s t r a i n i n g assembly i n t h i s case. The compressive devices were placed 3" from the lower end of the d r i l l holes. The two bolts were then loaded to 10 tons each. I s o c l i n i c s , normal and oblique isochromatics as well as the s t r a i n gauge readings were recorded, and the stresses along and normal to the l i n e of symmetry were calculated. Figure No 18 shows a composite photo of one of the oblique incidence isochromatics, (as i t was much cle a r e r than the normal incidence case due to the low fringe orders). Figure No 19 shows the stresses along and normal to the l i n e of symmetry. 5-5 Expansion s h e l l anchored bolt with a lower compressive  device on the rock model; Two 24" long, 5/8" 0 of high t e n s i l e strength s t e e l - 31 -F i g u r e No .15 Normal Incidence Isochromatics, P l a s t i c  Model, Glue Anchored B o l t s With Lover  Compressive Device. - 5 2 -1 1 I ' + O.S 0 -o.s -i.o -n,,^ F i g u r e No 1,6 L a t e r a l and L o n g i t u d i n a l S t r e s s D i s t r i b u t i o n  Between Two Glue Anchored B o l t s With Lower  Compress ive D e v , P l a s t i c M o d e l , P a t t e r n o f . -F i g u r e No 17 The Lower Compressive D e v i c e . 1 - Hollow Wedge. 2 - S h e l l Leaves. 3 - Pusher. 4 - End P l a t e s F o r The B o l t Stressmeter, 5 - B o l t S t r e s s m e t e r . 6 - T i g h t e n i n g Nut. 7 - The Roof B o l t . - 34 -were expansion shell-anchored i n two 12" spaced 18" long 1.2 0 d r i l l holes. The compressive devices were f i t t e d 3" from the lower end of the d r i l l holes and the bolts were loaded to 6 tons each. I s o c l i n i c s , normal and oblique i n c i -dence isochromatics as well as the s t r a i n gauges readings were recorded and the stresses along and normal to the l i n e of symmetry were calculated. Figure No 20 shows the normal incidence isochromatics. Figure No 21 shows the d i s t r i b u -t i o n of the l a t e r a l as well as the l o n g i t u d i a l stresses along and normal to the l i n e of symmetry. 6- Discussions and Conslusions f o r The 2nd Group of Tests As shown i n Figures No 16, 19',and 21 the lower com-pressive device has a remarkable e f f e c t on i n c r e a s i n g the l a t e r a l compression i n the lower zone of both the p l a s t i c and the rock models. I t should be noted here, that i n the case of roof beams, t h e i r response to t h i s compressive stress d i f f e r s according to the depth at which t h i s stress i s applied. In the case of an expansion s h e l l anchored b o l t with a lower compressive device, small l o n g i t u d i n a l compressive stresses were observed i n the middle of the bolt length, while with the glue-anchored bolt there was no l o n g i t u d i -n a l compressive stress observed. This i s due to the f a c t that the bolts i n our case are only 18" long i n the rock and spaced by 12" i n the case of the expansion s h e l l - a n -chored ones, and 24" i n the case of the glue-anchored b o l t s . This shows that the higher the r a t i o of the bolt length/sp-acing, the higher the l o n g i t u d i n a l compressive s t r e s s . This r a t i o was found by Lang^ to be 3/1 f o r the compressive l o n g i t u d i n a l stresses to cover a depth of 2/3 of the bolt F i g u r e No f g 4 5 ° Oblique Incidence Isochromatics, Rock  Model, Epoxy Anchored Bolts With Lower  Compressive Dev. 24" Spacing, 10 Tons Load - 56 -dorYB/ri/Of/v/h-LATERAL * 20 ft / I /tz" y / If-1 8" \ 6" 4" \ . ^2oo +/oo o .too .zoo _3oo _<H>O psi Figure No '19 L a t e r a l and L o n g i t u d i n a l S t r e s s D i s t r i b u t i o n  Between Two Epoxy Anchored B o l t s With Lower  Compressive Dev, 10 Tons Load, 24" Spacing - 37 -F i g u r e No 20.. Normal Incidence I s o c h r o m a t i c s , Rock Model,  Expansion S h e l l Anchored B o l t s With Lower  Compressive Dev. 12" Spacing, 6 Tons Load. - 39 " . LONOTUOINIH, r \ Lf)r££RL / \ - \ * > It A 8" / 1 \ V 0 I / /00O *»oo 0 - fOO -lata -Ifaa - 2ooo -2foe - 5 » » o psc F i g u r e No 2 T L a t e r a l and L o n g i t u d i n a l S t r e s s D i s t r i b u t i o n Between Two 3xpan . S h e l l Anchored B o l t s Wi th Lower Comp. Dev i ce , 6 Tons Load , 12" S p a c i n g - 39 -l e n g t h . This conforms .with the p l a s t i c model r e s u l t s . The use of the epoxy-anchored b o l t with the compressive device f i x e d at i t s lower end secures the advantages of the epoxy-anchored b o l t w i t h added l a t e r a l compression around the d e v i c e . This w i l l i n c r e a s e the shear s t r e n g t h of the rock and i n c r e a s e s the s t a b i l i t y of the r o o f s s t r u c t u r e . Figure No 22 ( l i g h t curve ) g i v e s the p o s s i b l e d i s -t r i b u t i o n of the t a n g e n t i a l s t r e s s e s due to the expansion s h e l l . The experimental r e s u l t s gave the two extreme ends of the curve. The curve was constructed p a r a l l e l to the to the curve given by the equation, crft = P r 2 This equation gives the s t r e s s d i s t r i b u t i o n i n the w a l l s o f a t h i c k c y l i n d e r , o f i n t e r n a l r a d i u s r , i n t e r n a l h y d r o s t a t i c pressure P, i n f i n i t e outer diameter, and zero 2 outer s t r e s s . Where, P = The t r a n s v e r s e expansion s h e l l s t r e s s . = b o l t p u l l x 1.5  contact area bet. s h e l l l eaves and d r i l l - h o l e w a l l s a = d i s t a n c e from the d r i l l - h o l e c e n t e r , r = r a d i u s of the d r i l l - h o l e . On the same f i g u r e the heavy curve g i v e s the p o s s i b l e t a n g e n t i a l s t r e s s d i s t r i b u t i o n due to the expansion s h e l l a f f e c t e d by a t a n g e n t i a l f i e l d s t r e s s of_2000 p s i . As shown, the f i e l d s t r e s s l i m i t s the t e n s i l e s t r e s s e s due to the anchor to the f i r s t i n c h i n the d r i l l - h o l e w a l l s , and redu-ces to a great extent the hazards of rock f a i l u r e around - 40 -/6 4 11 H> -F i g u r e No 22 P o s s i b l e T a n g e n t i a l S t r e s s D i s t r i b u t i o n  Due To Expans ion S h e l l Anchor In Rock  Mode l . B o l t P u l l 10 t o n s , Spac i ng 24" With and Wi thout T a n g e n t i a l F i e l d S t r e s s A Exfe&iMENT/H. RESULTS. Wmvor Fiet-D STXBSS. U,rY ?nn» />// T6L Fmt-O STKESS 0 - 41 -the anchor. I n t h i s s m a l l zone s u b j e c t e d to the t e n s i l e s t r e s s around the d r i l l - h o l e , even though the r o c k i s f r a c t u r e d , y e t i n f i r m r o c k s i t does not f a i l completely thereby t r a n s m i t t i n g the anchor p r e s s u r e to the r o c k around. Depending on the r o c k s t r e n g t h , the extent o f the f r a c t u -r e d zone v a r i e s . I n weak r o c k s , i t extends beyond the l i m i t where the f r a c t u r e d rock can no l o n g e r t r a n s m i t enough anchor p r e s s u r e t o the s u r r o u n d i n g rock, and the expansion s h e l l b e i n g o f v e r y l i m i t e d l a t e r a l range, can n o t expand enough to induce adequate l a t e r a l s t r e s s e s to h o l d the b o l t a x i a l l o a d , and the anchorage f a i l s . NOTE ABOUT THE STRESSES IN THE PLASTIC MODEL : As can be n o t i c e d i n the f i g u r e s c o n t a i n i n g the s t r e s s d i s t r i b u t i o n i n . t h e p l a s t i c model, s p e c i a l l y i n F i g u r e No 12, the t e n s i l e s t r e s s e s are s l i g h t l y h i g h e r than they should be due to the b o l t s t r e s s e s . T h i s excess o f t e n s i o n i s caused by the u p - b u c k l i n g o f the model which i s onl y 1/4" t h i c k and 24" x 24" s u r f a c e a r e a . However, such t e n s i l e s t r e s s e s were assessed and found o f ve r y s m a l l magnitude ^ compared w i t h the b o l t s t r e s s e s , and were t h e r e f o r e n e g l e c t e d . The p l a s t i c model was assumed to be a p l a n e . In the rock model, on the o t h e r hand, the depth o f the rock s l a b , t h e symmetry of l o a d i n g , the c o n f i n i n g e f f e c t o f the c o n s t r a i n i n g box, and the use o f s h o r t b o l t s , p r o h i b i t e d the p o s s i b i l i t i e s f o r such b u c k l i n g to take p l a c e . - 42 -POSSIBLE APPLICATIONS The f o r e g o i n g shows t h a t the compressive device can apply e f f i c i e n t d i r e c t compressive s t r e s s e s on the surrounding r o c k s . P o s s i b l e a p p l i c a t i o n of such d e v i c e , used alone o r f i x e d to the r o o f b o l t s are given below. 1- Cases of Roof Beams; I n many cases s p e c i a l l y i n s t r a t i f i e d rocks, the 3 4 r o o f a c t s as a f r e e l y supported simple beanr* , w i t h con-s t r a i n e d ends and back. I n such cases, r o o f b o l t i n g can s t a b i l i s e the r o o f beam i n the f o l l o w i n g ways; 1-1 Beam B u i l d i n g ; A p p l y i n g normal f o r c e to the shear planes i n c r e a s e s the shear s t r e n g t h of the rock mass and binds the d i f f e r e n t b l o c k s o r m u l t i p l e l a y e r s of the immidiate r o o f i n t o a mono-l i t h i c beam. This beam i s i n h e r e n t l y stronger than the i n d i v i d u a l b l o c k s or separate l a y e r s . 1-2 P r e s t r e s s ; Since rock i n s i t u i s g e n e r a l l y under s t r a i n , i t tends to r e l a x and expand i n t o any opening which may be c r e a t e d . This movement induces d i f f e r e n t i a l s t r e s s e s which may r e s u l t i n s h e a r i n g the rock mass. Tensioned r o o f b o l t s , i f placed s h o r t l y a f t e r b l a s t i n g , induce compressive s t r e s s e s i n the rock mass and r e s t r a i n i t from moving i n t o the opening and d i r e c t the movement l a t e r a l l y . The rock being c o n s t r a i n e d a t both ends, b u i l d s up a l a t e r a l compressive s t r e s s which helps to i n c r e a s e the shear s t r e n g t h of the rock mass and s t a b i l i s e s the r o o f . This a c t i o n has been found more n o t i c e a b l e i n f r a c t u r e d rocks where f r a c t u r e f i l l i n g s a c t as l u b r i c a n t - 43 -f o r the wedging a c t i o n which takes p l a c e i n f r a c t u r e d r o c k s . 1-3 Roof beams which .lack h o r i z o n t a l compressive s t r e s s to compensate f o r the t e n s i l e f l e x u r a l s t r e s s e s i n the lower f i b r e s , tend to sag i n t o the opening. Epoxy-ancho-red b o l t s w i t h l e n g t h adequate to create a m o n o l i t h i c beam o f s u i t a b l e depth, f i t t e d w i t h the compressive devices i n the:lower t e n s i l e zone are u s e f u l i n b u i l d i n g up a mono-l i t h i c beam as w e l l as compensating f o r the t e n s i l e f l e x u r a l s t r e s s e s . Thus they form a s t a b l e r o o f beam. 1-4 I n many cases r o o f beams w i t h s u i t a b l e depths are n a t u r a l l y formed over the opening. I f these beams l a c k h o r i z o n t a l compression to keep them from sagging i n t o the opening, the compressive device i f f i x e d alone i n the lower t e n s i l e zone of the beam can give the r e q u i r e d support. F i g u r e No 23 shows the a c t i o n of d i f f e r e n t r o o f b o l t designs on the simple beam r o o f . 1- 5 I n some cases where the h o r i z o n t a l f i e l d s t r e s s e s and t h e i r c o n centrations due to the opening are very h i g h , and the opening width i s l i m i t e d f o r some reason, ;the r o o f beam being c o n s t r a i n e d to move upwards, i t t h i c k e n s i n the middle and e v e n t u a l l y buckles i n t o the opening and f a i l s under c r u s h i n g and s h e a r i n g . I n these cases standard epoxy-anchored b o l t s would s u i t the s i t u a t i o n . 2- Gases o f No Roof Beams I n some cases s p e c i a l l y i n f r a c t u r e d r o c k s, r o o f s do not behave as beams. I n these cases, i n gener a l , a d e s t r e -ssed zone appears close to the ro o f w i t h another compressed zone behind i t . I n these cases, b o l t i n g s t a b i l i s e s the ro o f - 44 -f l e x u r e s t r e s s e s expan. s h e l l b o l t s t r e s s e s a - Expansion s h e l l anchored b o l t . combined s t r e s s e s f l e x u r e s t r e s s e s £ b- Glue anchored b o l t * glue anchored combined b o l t s t r e s s e s s t r e s s e s f l e x u r e s t r e s s e s Gomp.Device a t lower 1/3 depth glued b o l t without end p l a t e combined s t r e s s e s F i g u r e No 2 J c- Glue anchored b o l t w i t h  lower compressive device. - 45 -i n the f o l l o w i n g ways; 2-1 P r e s t r e s s ; As d i s c u s s e d under 1-2. 2-2 To compensate f o r t e n s i l e s t r e s s e s due to the end p l a t e s and/or f o r the l a c k o f adequate l a t e r a l com-p r e s s i v e s t r e s s e s i n the decompressed zones, the compre-s s i v e d e v i c e s i f f i x e d on the b o l t s o r alone i n these zones, add the nec e s s a r y l a t e r a l compressive s t r e s s e s . A p p l i c a t i o n o f Mohr Theory o f F a i l u r e t o Mine Roofs. Depending on the magnitude of the l a t e r a l f i e l d s t r e s s , i t s c o n c e n t r a t i o n , the shape o f the opening and i t s dimensions, the s t r e s s e s a c t i n g on the r o o f change. But i n g e n e r a l , they can be r e s o l v e d i n t o h o r i z o n t a l and v e r t i c a l compressive s t r e s s e s . The r o o f i n the g e n e r a l case c o n s i s t s o f f r a c t u r e d rock, w i t h a p r e f e r r e d shear plane whose angle o f i n t e r n a l f r i c t i o n i s 0, ( F i g u r e No 24) Case 1: I f the h o r i z o n t a l s t r e s s i s h i g h e r than the v e r t i c a l one. H o r i z o n t a l s t r e s s = - 0 7 , V e r t i c a l s t r e s s = - o-j As shown i n F i g u r e No 24, i f o^/ 0! r a"ki° i s over a c e r t a i n v a l u e , the Mohr c i r c l e c r o s s e s the f a i l u r e envelope and the r o o f f a i l s under e x c e s s i v e compression. The s o l u t i o n i n t h i s case i s to i n c r e a s e cr^  so t h a t the Mohr c i r c l e r e t r e a t s below the f a i l u r e envelope. T h i s can be a t t a i n e d by e i t h e r i n c r e a s i n g the span, o r by v e r t i -c a l b o l t i n g . The o-i needed to h o l d the r o o f i s c a l c u l a t e d from, - 46 -- 47 -<Ti = 2 S„ cot a - a\ cot a l o 2 where, S Q = the shear strength of the rock mass, a = 45° + i 0 Case 2: I f the v e r t i c a l stress i s higher than the h o r i z o n t a l one. Horizontal stress •= - o^ j ' V e r t i c a l stress = - o^ . As shown i n Figure No 24, at a c e r t a i n value f o r the r a t i o °1 / °2 ' ^ o n r c i r c l e crosses the f a i l u r e envelope and the roof f a i l s under shear f o r the lack of h o r i z o n t a l com-pression. The s o l u t i o n i n t h i s case i s to increase o~^  so that the Mohr c i r c l e r etreats below the f a i l u r e envelope. This can be attained by inducing d i r e c t l a t e r a l stress using the compressive devise. The same formula given i n case 1 i s used here to get the optimum magnitude of cr,. - 48--CONCLUSIONS 1 - The transverse compressive f o r c e s due to the expansion s h e l l anchor, unless they are d i s t r i b u t e d over a l a r g e area, are harmful to the medium s t r e n g t h and s o f t e r r o c k s . The expansion shell-anchored b o l t s are not e f f i c i e n t i n such rocks . However, high l a t e r a l f i e l d s t r e s s e s help to reduce t h i s e f f e c t to a l a r g e ' e x t e n t . The epoxy-anchored b o l t s are more e f f e c t i v e i n medium s t r e n g t h and s o f t e r rocks. 2- The d i s t r i b u t i o n of the s t r e s s e s due to the standard b o l t s i n d i c a t e s that they a r e ^ e f f e c t i v e l i h l b u i l d i n g : . u p a m o n o l i t h i c roof rock mass, but they are not as e f f e c t t i v e i n s t a b i l i s i n g the thus formed r o o f . 3 - Model t e s t s have i n d i c a t e d that the use of the compres- ^ s i v e devices alone or f i t t e d to the b o l t s i n the destressed zones, helps to i n c r e a s e roof rock s t a b i l i t y . 4 - In designing roof b o l t i n g systems, the d i r e c t i o n a l p r o p e r t i e s of the rock should be taken i n t o c o n s i d e r a t i o n . f - 49 -SUGGESTIONS FOR FURTHER WORK:." There i s no g e n e r a l agreement on the s t r u c t u r a l "behaviour o f the mine r o o f . Model work done so f a r has not achieved proper d u p l i c a t i o n o f the i n s . i t u c o n d i t i o n s of mine r o o f s . Measurements on e x i s t i n g mine r o o f s have not been s u f f i c i e n t l y d e t a i l e d to i n t e r p r e t t h e i r t r u e "behaviour. I t i s suggested t h a t d e t a i l e d measurements "be c a r r i e d out to determine the a c t u a l s t r e s s d i s t r i b u t i o n i n mine r o o f s . R e l a t i o n s between such s t r e s s d i s t r i b u t i o n and time l a p s e , advance of the fa c e and b l a s t i n g shocks' should a l s o be f i r m l y e s t a b l i s h e d . Such f u t h e r f i e l d i n v e s t i g a t i o n ' s should permit rock b o l t i n g p a t t e r n s to :.be e s t a b l i s h e d on s c i e n t i f i c b a s i s r a t h e r than the present emperical approaches to the s u b j e c t . From the author's i n v e s t i g a t i o n s on a two d i m e n s i o n a l , p h o t o e l a s t i c p l a s t i c model and a lim e - s t o n e rock model, i t was found that the i n s e r t i o n o f a compressive d e v i c e designed by the author, superimposes a compressive l a t e r a l s t r e s s , on the a l r e a d y e x i s t i n g s t r e s s f i e l d . -The p r a c t i c a l a p p l i c a t i o n s o f t h i s compressive d e v i c e , alone o r f i t t e d to rock b o l t s , i n s t a b i l i s i n g mine r o o f s i s proposed as w a r r a n t i n g i n v e s t i g a t i o n . - I n the course o f such i n v e s t i g a t i o n s r e q u i s i t e m o d i f i c a t i o n s and; r e f i n e m e n t s ' t o the de s i g n o f t h i s compressive d e v i c e would - b e - - i d e n t i f i e d . - 50 -REFERENCES 1- T. A. Lang, Theory and Practic e of Rock Bo l t i n g , AIKE Transactions v o l 220, 1961, pp. 333 - 348. . 2- S. Timoshenco and J . N. Goodier,'Theory of E l a s t i c i t y , .McGraw-Hill Book Company Inc., 1951, .pp. 58 - 60. • 3- A. V. C o r l e t t and C. L. Emery, Prestress and Stress R e d i s t r i b u t i o n i n Rocks Around a Mine Opening, CIM B u l l e t i n , June 1959, pp. 372 - 383. -4 - L. A. Panek, P r i n c i p l e s of Reinforcing Mine Roofs With • Roof Bolts, USBM, RI 5156, March 1956. 5- D. C. Drucker, Separation of The P r i n c i p a l Stresses by Oblique Incidence, Journal.of Applied • Mechanics, September 1943, p. A 156. 6- Parsons 2., Design and Development of a Rock Bolt-Anchored by Explosive Forming, USBM, RI 6250, 1963. .7-' T. A. Lang, Rock Behaviour and Rock B o l t i n g i n Large Excavations, Symposium on Underground Power Stations,.ASCE Convention, New York, October 1957. 8- L. A. Panek, Design of B o l t i n g Systems to Reinforce Bedded Mine Roofs, USBM, RI 5155,.March 1956. 9- B. Parsons & L. Osen, Transverse Force Due to the Expansion S h e l l , USBM, RI 7087, July 1968. In the preparation of t h i s thesis, f i f t y one references dealing with rock b o l t i n g i n general were studied. Only the ones l i s t e d above are considered to be relevant to the s p e c i f i c subject under discussion. - 51 -APPENDIX No I C a l i b r a t i o n of The P l a s t i c Materials 1 - The P l a s t i c Model ; A 2" 0 disk was cut from the same material of the p l a s t i c model and loaded d i a m e t r i c a l l y . The f r i n g e order was observed at the center of the disk. As the f r i n g e order i s the measure of 0*^  - cr^ , at the center of the disk t h i s i s given by, ~- ~ 8 P N f ° i " °2 = TdFt = T Where, P = diametric load applied l b s . d = disk diameter, i n . t = disk thickness, i n . N = fri n g e order. f - stress fringe value of the p l a s t i c , p s i . i n / f r Therefore, f = a As ~ - r i s a constant, and = 1 .274 i n our case, TT Q thus f = 1.274 | Recording the load applied against the f r i n g e order at the center of the disk, the slope of the curve thus obtained gives the value of P/N , from which f can be calculated. Figure No 25 ( the thick l i n e ) shows that the slope of the best f i t t i n g l i n e i s 47.1 . Thus, f = 1.274 x 47.1 = 59.9954 take 60.0 p s i . i n / f r i n g e . 2- The P l a s t i c Coating of The Rock Model : Using the same procedure and c a l c u l a t i o n , f was found to be 56 p s i . i n / f r i n g e , as i n Figure No 25 ( t h i n l i n e ). F i g u r e No 25 C a l i b r a t i o n Chart f o r The P l a s t i c M a t e r i a l s - 53 -APPENDIX No II Model Rock Properties : To l i m i t the stresses applied to the rock model to the permissible l e n i a r range, and to calculate the stresses from the s t r a i n s recorded from the s t r a i n gauges, the comp-ressive and t e n s i l e strengths of the rock together with the modulus of e l a s t i c i t y and Poisson's r a t i o should be known. Experiments were carr i e d out on samples core d r i l l e d alog and normal to the d i r e c t i o n of the bolt d r i l l - h o l e s . 1- Tensile Strength Test : The B r a s i l i a n test was used. Five disks 17/16" 0 and 1/2" thick were tested f o r each d i r e c t i o n . The f a i l u r e load was recorded and the t e n s i l e strength was calculated from, T = - ^ " t where, P = the load at* f a i l u r e , l b s . d = disk diameter, i n . t = disk thickness, i n . For the reasons of research ( l i m i t s of strength ), the lowest value was considered, thus; T p a r a l l e l to the bolt d i r e c t i o n = 1200 p s i . T normal to the bolt d i r e c t i o n = 1020 p s i . 2- Compressive Strength Test : Unia x i a l compressive t e s t s were conducted on core cylinders of 17/16" 0 and 17/16" long. F a i l u r e loads were recorded and the compressive strength was calculated from, C = P/A where, :P = load at f a i l u r e , and A = area of the sample c.s.% C i n both d i r e c t i o n s was the same and = 13500 p s i . .- 54 -3- Modulus of E l a s t i c i t y and Poisson's Ratio : These tests were carried out on samples 1.583" 0 and 3.75" long. Two single s t r a i n gauges were f i x e d d i a m e t r i c a l l y opposite at the midlength of the cylinders, one p a r a l l e l to the axis and the other normal to i t . Load was applied at the rate of 100 lb/sec t i l l 8000 l b s . Strains i n every s t r a i n gauge were recorded every 1000 l b s i n t e r v a l . The load was then released gradually and again the s t r a i n s were recorded every 1000 l b s . Load was raised a f t e r that t i l l f a i l u r e reco-rding s t r a i n s every 2000 l b s . The calculated E and v i n both d i r e c t i o n s were almost the same f o r the secant value along the 12000 p s i range. E = 4.1 x 10 6 p s i . , and the Poisson's r a t i o ( v ) =0.28. However the rock tends to be weaker when tested normal to the d r i l l - h o l e d i r e c t i o n s . - 55 -APPENDIX No I I I The Rock M a t e r i a l R e s i d u a l S t r e s s e s A cube of 2" x 2" x 2" was cut. from the modei mother block and o r i e n t e d a c c o r d i n g to the model edges. Three p l a s t i c d i s k s 1 " 0 were glued w i t h a r e f l e c t i v e glue to three o r t h o g n a l faces meeting at one corner. The rock was l e f t one day to r e l a x . A f t e r t h i s p e r i o d , the p l a s t i c d i s k s were t e s t e d under the normal and o b l i q u e i n c i d e n c e p o l a r i s c o p e s , yet two faces showed almcst absence of s t r e s s w h i l e the t h i r d showed a f e e b l e i n d i c a t i o n of the r e l a x a t i o n s t r e s s e s . A f t e r a p e r i o d of 7 days, the t e s t was conducted again, and the same r e s u l t s were obtained, w i t h a s l i g h t i n c r e a s e i n s t r e s s e s i n the t h i r d f a c e . Although the magnitude of the s t r e s s could not be detected, yet the the d i r e c t i o n of the s t r e s s v e c t o r was found to be i n c l i n e d to t h i s block surface w i t h 60° i n the plane normal to the d r i l l h o l e s . The f e e b l e amout of s t r e s s detected i n ' t h i s ' r o c k might be due to two main reasons, 1 - I t i s a recent chemical marine p r e c i p i t a t i o n . 2 - I t was cut from the quarry i n 6" s l a b s and l e f t to r e l a x ( cure') f o r l o n g time f o r the use as b u i l d i n g stones. . From the r e s u l t s of t h i s Appendix and the previous one, we can say that t h i s rock i s almost homogenious and f r e e from r e s i d u a l s t r e s s e s and i s i d e a l as a b u i l d i n g stone. For the purpose of our work, the rock p o s t u l a t e s the c o n d i t i o n s of medium rock. Absence of s t r e s s e s of s i z a b l e magnitudes, made i t p o s s i b l e to detect the s t r e s s e s due to the r o o f b o l t s without i n t e r f e r e n c e . However, the d i r e c t i o n a l p r o p e r t i e s might give some i n t e r f e r e n c e . - 56 -F i g u r e No 26 R e l a x a t i o n Tes t F i e l d S t r e s s D i r e c t i o n , - 57 -APPENDIX No I V SAMPLE CALCULATION Calculation of n. and n~ from n ., 1 2 01' n o2' and n n The case of the p l a s t i c model subjected to the stresses due to glue anchored bolts ( page 22, Figure No 12 ), and the l i g h t path was oblique to the normal to the l i n e of symmetry-by 45° • point n n n o- n 1 n 2 * a 1 2 3 4 5 6 7 8 9 10 11 12 1.51 0.67 0.78 1 .92 2.81 3.00 2.91 2.62 2.15 1 .65 1.17 0.75 0.30 1.25 0.55 0.75 2.06 2.90 3.00 3.00 2.70 2.13 1.58 1.01 0.40 0.15 inc inc inc i n c inc' i n c i n c i n c i n c i n c i n c i n c dec + 1.24 + 0.56 + 0.26 + 0.94 1 .50 1.80 1.60 1 .40 1.30 1.10 0.94 0.94 + + + + + + + + + 0.81 -0.26 - 0.11 - 0.52 - 0.93 - 1 .30 -'1.20 - 1.30 - 1 .20 - 0.85 - 0.55 -,0.23 + 0.19 + 0.51 +.n^ or + n^ means t e n s i l e stresses. - n^ or n^ means compressive stresses < These values were calculated Using the fbrmulee n 1 = ]/2 n 2 = V2 n o1 - n.. n n 0 + n o2 n n n = n1 - n 2 To get the stresses multiply n^ or n 2 by F 2 t As ?_ i s a constant, the graph showing the d i s t r i b u t i o n 2t of n^ and n 2 gives the same d i s t r i b u t i o n of cTj and cr^ . The deailed technique of measuring and of the calculations are given i n the Laboratory Manual used i n t h i s department. - 58 -• APP3NDIX Ko V  ERRORS 1- P l a s t i c Model In p h o t o e l a s t i c work, so l o n g as the model m a t e r i a l i s chosen to be s e n s i t i v e enough f o r the purpose, f r e e from creep and time-edge e f f e c t and r e s i d u a l s t r e s s e s , has reason-a b l e u l t i m a t e s t r e n g t h compared wi t h the lo a d s expected to be used, and so l o n g as these l o a d s do not exceed the l i n e a r l i m i t o f the m a t e r i a l s t r e s s / s t r a i n curve, then the e r r o r s are l i m i t e d i n the f o l l o w i n g ; 1- P e r s o n a l judgement f o r compensation while u s i n g the a n a l y s e r . I n our case u s i n g an a n a l y s e r s e n s i t i v e to 0.01" of a f r i n g e the e r r o r can be l i m i t e d to + 0.025 f r i n g e i n f l a t g r a d i e n t s , and + 0.01 i n steep g r a d i e n t s . 2- V/hen u s i n g o b l i q u e i n c i d e n c e r e f l e c t i v e method, we are compensating f o r the average s t r e s s e s o v e r a l e n g t h of 2t tan© i n the plane o f the model s u r f a c e , and n o t to the s t r e s s a t the midpoint o f t h i s l e n g t h , F i g u r e No 27. I t i s c l e a r from the f i g u r e t h a t t h i s e r r o r i s s i g n i f i -cant when the f r i n g e g r a d i e n t i s s t e e p . On the o t h e r hand, when the g r a d i e n t i s f l a t , the e r r o r s a r e s m a l l . T h i s e r r o r , however, can be minimized by r e d u c i n g the model t h i c k n e s s . I n t r a n s m i s s i o n models, t h i s e r r o r i s cut i n t o h a l f . F o r t h i s reason, the most a c c u r a t e r e s u l t s are o b t a i n e d from normal i n c i d e n c e and one o b l i q u e i n c i -dence where the i s o c h r o m a t i c s a re normal to the l i g h t p a t h . I n our case the model t h i c k n e s s was 1/4", and the f r i n g e gradients'were g e n e r a l l y f l a t . The e r r o r i n r e a d i n g i n hi 1 ! /1 i ! ! / i , i , i i l\ I : • ! i ! i D/STONCF ON TH* f/?ce o r Tie Mooeu F i g u r e Ho 27 E r r o r Due To O b l i q u e I n c i dence Read ing In  F l a t And Steep F r i n g e G r a d i e n t s A f t e r D r u c k e r 2 2 t h i s area i s estimated by 57° • 3- Refraction of the l i g h t entering and leaving the p l a s t i c obliquely from the a i r . This i s eliminated i n our case by using a 45° prism, and using the immersion method. Hoever, Drucker p considers that errors due to r e f r a c t i o n are n e g l i g i b l e . 4 - The error i n s e t t i n g the angle of o b l i q u i t y . In our case a l i g h t s t e e l structure was s p e c i a l l y b u i l t to hold the l i g h t source, the lenses, the camera, and the analyser i n r i g i d 45° p o s i t i o n s . 5- The error i n s e t t i n g p r i n c i p a l stresses d i r e c t i o n p a r a l l e l to the l i g h t path. In our case the loads are symmetric, thus the d i r e c t i o n s of the p r i n c i p a l stresses are along and normal to the l i n e of symmetry, and there was no much trouble s e t t i n g t h i s l i n e along the l i g h t path. P o s s i b i l i t i e s of error i n t h i s area are very l i m i t e d . 6- I t should be noted here that the epoxy materials are generally teperature s e n s i t i v e e Errors due to t h i s , can be reduced by keeping the room teperature as stable as possible, and keeping the epoxy model away from the reach of the l i g h t source heat. In general we can estimate the t o t a l experimental error i n our work to be l e s s than 10$, which i s an accepta-ble fi g u r e i n t h i s p r a c t i c e . In the p l a s t i c model, r e s u l t s obtained from f i v e readings were averaged using the standard deviation method, with the i n t e r v a l procedure. The average c o e f f i c i e n t of v a r i a b i l i t y was i 9.785°, with 80$ confidence l i m i t . -•61 -2- Rock Model 2-1 P h o t o e l a s t i c measurements ; The same e r r o r s d i s c u s s e d above, a p p l y i n t h i s case f o r the s t r e s s e s c a l c u l a t e d from p h o t o e l a s t i c measurements. I n exess, t h e r e i s the e r r o r o f o b l i q u e l o a d i n g . S i n c e the d r i l l - h o l e c e n t e r s are 3" lower than the p l a s t i c sheet plane, the s t r e s s e s r e a c h i n g i t are o b l i q u e . T h i s tends to bulge the r o c k s u r f a c e upwards i n the a r e a f r e e from c o n s t r a i n i n g . T h i s i s shown c l e a r l y by the s t r e s s p a t t e r n i n F i g u r e No 23, where the p a t t e r n resembles t h a t o f a bent beam ubder o b l i q u e f o r c e . T h e r e f o r e , e r r o r s i n t h i s case are estimated to be about 10$. 2-2 S t r a i n gauges r e a d i n g s t A l l the p o s s i b l e p r e c a u t i o n s were taken i n embedding the s t r a i n gauges i n the c e n t e r l i n e o f the rock b l o c k . F i v e a c r y l i c cement dolomite powder mixures were t e s t e d and the mixure o f 50/50 was chosen as i t gave almost the same c h a r a c t e r i s t i c s as the r o c k . T h i s cement mixure was used i n f i l l i n g the d r i l l - h o l e s where the s t r a i n gauges were put, to a v o i d s t r e s s c o n c e t r a t i o n around them. To reduce the e r r o r due to the e f f e c t o f the heat evolved by the s t r a i n gauges on the a c r y l i c cement, low heat gauges were used. Budd s w i t c h box and s t r a i n i n d i c a t o r were used to g i v e r e a d i n g s up to 1 u " / i n . A l l c o n n e c t i o n s were s o l d e r e d . I n s p i t e o f a l l these p r e c a u t i o n s , the s t r a i n r e a d i n g s were h i g h l y d r i f t i n g . The average d r i f t was 30 u " / i n . As the s t r e s s e s i n t h i s case are c o m p a r a t i v e l y s m a l l , - 62 -such b i g d r i f t i n t r o d u c e s an e r r o r i n the range o f 5 0 $ . T h e r e f o r e , the s t r a i n gauges r e a d i n g s were d i s c a r d e d . A l l s t r e s s d i s t r i b u t i o n curves i n t h i s work are based wholly on the p h o t o e l a s t i c measurements. 

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