1、Analytical models for rock bolts. C.L*,Stillborg Abstract Three analytical models have been developed for rock bolts: one for bolts subjected to concentrated pull load in pullout tests, one for bolts installed in uniformly deformed rock masses, and one for bolts subjected to the opening of individua
2、l rock joints. The development of the models has been based on the description of the mechanical coupling at the interface between the bolt and the grout medium for grouted bolts, or between the bolt and the rock for frictionally coupled bolts. For rock bolts in the pullout tests, the shear stress o
3、f the interfaces exponentially with increasing distance from the point of loading when the deformation is compatible across the interface. Decoupling may start first at the loading point when the applied load is large enough and then propagate towards the far end of the bolt with a further increase
4、in the applied load. The magnitude of the shear stress on the decoupled bolt section depends on the coupling mechanism at the interface. For fully grouted bolts, the shear stress on the decoupled section is lower than the peak shear strength of the interface while for fully frictionally coupled bolt
5、s if is approximately the same as the peak shear strength. For rock bolts installed in uniformly deformed rock, the loading process of the bolts due to rock deformation has been taken into account in developing the model. Model simulations confirm the previous findings that a bolt in situ has a pick
6、-up length, an anchor length and neutral point. It is also revealed that the face plate plays a significant role in enhancing the reinforcement effect. In jointed rock masses, several axial stress peaks may occur along the bolt because of the opening of rock joints intersecting the bolt. 1. Introduc
7、tion Rock bolts have been widely used for rock reinforcement in civil and mining engineering for a long time. Bolts reinforce rock masses through restraining the deformation within the rock masses. In order to improve bolting design, it is necessary: to have a good understanding of the behaviour of
8、rock bolts in deformed rock masses. This can be acquired through field monitoring, laboratory tests, numerical modeling and analytical studies. Since the 1970s, numerous researchers have carried out field monitoring work on rock bolts installed in various rock formations. Freeman performed pioneerin
9、g work in studying the performance of fully grouted rock bolts in the Kielder experimental runnel. He monitored both the loading process of the bolts and the distribution of his monitoring data, he proposed the concepts of “neutral point” “pick-up length” and “anchor length”. At the neutral point, t
10、he shear stress at the interface between the bolt and the grout medium is zero, while the tensile axial load of the bolt has a peak value. The pick-up length refers to the section of the bolt from the near end of the bolt (on the tunnel wall) to the neutral point. The shear stresses on this section
11、of the bolt pick up the load from the rock and drag the bolt towards the tunnel. The anchor length refers to the section of the bolt from the neutral point to the far end of the bolt (its seating deep in the rock). The shear stresses on this section of the bolt anchor the bolt to the rock. These con
12、cepts clearly outline the behaviour of fully grouted rock bolts in a deformed rock formation. Bjonfot and Stephanssons work demonstrated that in jointed rock masses there may exist not only one but several neutral points along the bolt because of the opening displacement of individual joints. Pullou
13、t tests are usually used to examine the anchoring capacity of rock bolts. A great number of pullout tests have been conducted so far in various types of rocks. Farmer carried out fundamental work in studying the behaviour of bolts under tensile loading. His solution predicts that the axial stress of
14、 the bolt (also the shear stress at the bolt interface) will decrease exponentially from the point of loading to the far end of the bolt before decoupling occurs. Fig.1(a) illustrates the results of a typical pullout test. Curve a represents the distribution of the axial stress along the bolt under
15、a relatively low applied load, at which the deformation is compatible on both sides of the bolt interface. Curve b represents the axial stress along the bolt at a relatively high applied load, at which decoupling has occurred at part of the bolt interface. Fig.1(b) shows the axial stress along a roc
16、k bolt installed in an underground mine drift. It is seen from this figure that the distribution of the axial stress along the section close to the borehole collar is completely different from that in pullout tests. However, along the section to the far end of the bolt, the stress varies similarly t
17、o that in pullout tests. The reason 510155 15 25D i s t a n c e t o b o r e h o l e c o l l a r ( c m )Axial stress on steel bar(MPa) ( a )D e c o u p l e d s e c t i o nD i s t a n c e t o b o r e h o l e c o l l a r ( c m )Axial stress (MPa)50501 0 01 5 0( b )2 0 0ab2 0 0 Fig.1 Distribution if the
18、 axial stress (a) along a grouted steel bar during pullout test, after Hawkes and Evan, and (b) along a grouted rock bolt in situ after sun for these results is that bolts in situ have a pick-up length and an anchor length, while bolts in pullout tests only have an anchor length. It is thought that
19、the relative movement between the rock and the bolt is zero at the neutral point. In the solution by Tao and Chen, the position of the neutral point depends only on the radius of the tunnel and the length of the bolt. That solution was implemented in the analytical models created by Indraratna and Kaiser and Hyett et.al. It seems that Tao and Chens solution is valid only when the deformation is compatible across the bolt interface. When decoupling occurs, the position of the
