A prognostic model of side friction of rock bolt anchoring section based on associated flow law

Chen J., Liu L., Zeng B., Tao K., Zhang C., Zhao H., Li D., Zhang J.

To better understand the bonding failure at the contact between the bolt shank and anchoring agent, we developed a constitutive model of fully bonded rock bolts, in which the relative movement of the contact was considered. A bond coefficient factor was proposed to calculate the longitudinal displacement of the anchoring agent at the contact between the bolt shank and anchoring agent. The credibility of the developed model was demonstrated with three independent experimental pulling tests. A highlight of this model is that most input arguments can be acquired and calibrated directly from the experimental pulling data. Based on the developed model, a sensitivity analysis was performed. The influence of the bond coefficient and residual bond strength on the anchorage performance of bolt shanks was evaluated. The results revealed that the bond coefficient had a direct relationship to the anchorage performance of bolt shanks. The larger the bond coefficient is, the higher the bond capacity of the bolt shanks. However, there was a certain influencing range for the bond coefficient. Once the bond coefficient was beyond that range, the bond coefficient had a marginal effect on the anchorage performance of the bolt shanks. Moreover, when the residual bond strength equalled the bond strength, fully bonded bolts were likely to show constant resistance behaviour.

Pang D., He K., Xu Y., Chang J., Niu X., Li C.

To study the evolution law of axial force and shear stress of a full-length anchorage bolt in a rectangular roadway during roadway driving and working face mining, based on the stress analysis of the bolt, considering the elastic parameters and geometric size of the bolt, the effect of a bearing plate on surrounding rock, roadway cross-section shape, roadway deformation degree, and roadway elastic parameters, elastic mechanics and mathematical analysis methods were used to establish the mechanical model describing the interaction between the bolt and surrounding rock, and the mechanical formulas for calculating the axial force and shear stress of the bolt were derived. Taking the mining roadway of 1,131(1) working face in the Zhujidong coal mine of the Huainan mining area as the engineering background, the axial force and shear stress of the bolt in the middle of the roof and side of the rectangular roadway with the advance of driving face and working face were analyzed. The mechanical model and theoretical analysis results are verified by installing force measuring bolts with the same mechanical properties as the field and observing the real axial force distribution of the bolts.

Wang J., Apel D.B., Xu H., Wei C., Skrzypkowski K.

In this paper, a 2D distinct element method (DEM) model of a deep tunnel in an underground coal mine is built to thoroughly evaluate the effects of yielding (D-bolt and Roofex) and the traditional rockbolt (fully resin-grouted rebar) on controlling self-initiated strainbursts. The occurrence of self-initiated strainbursts is judged based on the stiffness difference between the loading system and rock masses for the first time. The results suggest that the total deformations of the tunnel supported with Roofex and resin-grouted rebar are 1.53 and 2.09 times that of D-bolts (1411 mm). The average velocities of detached rock blocks in the tunnel supported with Roofex and resin-grouted rebar are 3.22 and 3.97 m/s, respectively, which are much higher than that of D-bolts (0.34 m/s). 13 resin-grouted rebar bolts are broken during the strainburst, while D-bolts and Roofex survive. Compared with Roofex (295.16 kJ) and resin-grouted rebar (125.19 kJ), the D-bolt can reduce the most kinetic energy (469.30 kJ). D-bolt and resin-grouted rebar can maintain high axial force levels (214.87 and 151.05 kN) during strainbursts. Both Roofex and resin-grouted rebar fail to control strainbursts. The bolt number significantly influences the control effects of yielding rockbolts on strainbursts. 9 and 12 D-bolts cannot control the strainburst, while 15 and 18 D-bolts can make the tunnel stable. In addition, the detachment and ejection of rocks between rockbolts can be well restrained using surface retain elements, e.g., steel arch. This study highlights the usage of numerical modeling methods in assessing the performance of yielding rockbolts, which can be served as a promising tool to improve and optimize the design of rock supporting in burst-prone grounds.

Guo X., Zheng X., Li P., Lian R., Liu C., Shahani N.M., Wang C., Li B., Xu W., Lai G.

The traditional anchoring method of bolts has insufficient control over the surrounding rock of the coal roadway. Based on this background, full-stress anchoring technology of bolts was proposed. Firstly, a mechanical relationship model of a bolt-drawing, anchoring interface was established to obtain the equations of the axial force and obtain shear stress distribution as well as the decreasing-load transfer law of the anchoring section of bolts. Through studying the prestress-loading experimental device of bolts, we found that increasing the initial preload could increase the axial force under the same conditions and the retarded anchoring section could control the axial-force loss of bolts in the middle of the anchoring section. Under the full-stress anchoring mode, the effect of applying a pre-tightening force was better than that of applying a pre-tightening force under traditional anchoring methods. Moreover, FLAC3D (Fast Lagrangian Analysis of Continua 3D; ITASCA (Ita sca International Inc), Minnesota, USA) numerical simulation calculation was performed. Under the full-stress anchoring mode of bolts, the increased anchoring length reduced the damage of the anchoring section, with a wider control range of the rock formation and higher strength of the compressive-stress anchoring zone. Based on the above research, four methods for applying the full-stress anchoring technology of bolts in engineering were proposed. The full-stress anchoring technology of bolts in the coal roadway has been applied in the support project of the return-air roadway at working face 3204 of the Taitou Coking Coal Mine of the Xiangning Coking Coal Group, Shanxi. The maximum moving distance of the roof and floor of the roadway was reduced from 200 to 42 mm, and the maximum moving distance on both coal sides was reduced from 330 to 86 mm. The full-stress anchoring technology of bolts was able to control the surrounding rock in the coal roadway.

Li Y., Tannant D.D., Pang J., Su G.

• Deformation process and failure behavior of bolts subjected to shear loading were investigated and revealed. • An analytical model that can consider the bolt shank experiences large (plastic) deformations subject to shear loading was developed. • The effect of several key parameters including bolt angle, rock mass strength, joint dilation angle, and bolt tensile strain on the ultimate bolt contribution was presented. Failures of rock bolts installed in jointed rock masses due to shear movement along weak joints in bedding rock slopes or underground caverns are common. Existing models to design rock bolts often only consider a rock bolt’s shear behavior in the elastic stage and ignore their larger non-elastic deformations, which significantly underestimates the bolt’s contribution to the joint shear resistance. Therefore, developing an analytical model capable of reflecting the plastic strain‑hardening of rockbolts subjected to large deformation is very necessary for more effective numerical simulation models as well as rock support design. An experimental investigation was conducted on grouted bolts subjected to joint shear movement. The bolt installation angle with respect to the joint was varied in the tests. Pairs of strain gauges attached to the surface of the bolt shank near the joint measured the bolt deformation during the shear testing. The deformation characteristics of the bolt and grout in the elastic and the plastic stages were evaluated. Based on the experimental measurements, a new analytical model to predict the bolt’s ultimate contribution to the shear resistance of a joint was developed. This model considers large deformations. The analytical model includes the influences of the bolt angle, rock mass strength, joint dilation angle, and bolt tensile strain. A comparison of the model predictions with results from large-scale tests and other existing methods shows good agreement with the tests and an improvement over existing methods.

Jahangir E., Blanco-Martín L., Hadj-Hassen F., Tijani M.

This paper proposes a new interface constitutive model for fully grouted rock-bolts and cable-bolts based on pull-out test results. A database was created combining published experimental data with in-house tests. By means of a comprehensive framework, a Coulomb-type failure criterion accounting for friction mobilization was defined. During the elastic phase, in which the interface joint is not yet created, the proposed model provides zero radial displacement, and once the interface joint is created, interface dilatancy is modeled using a non-associated plastic potential inspired from the behavior of rock joints. The results predicted by the proposed model are in good agreement with experimental results. The model has been implemented in a finite element method (FEM) code and numerical simulations have been performed at the elementary and the structural scales. The results obtained provide confidence in the ability of the new model to assist in the design and optimization of bolting patterns. • New interface constitutive model suitable for both rock-bolts and cable-bolts. • The new model is based on laboratory pull-out test results (in-house and external). • The interface radial behavior has no elastic component. • Model has been implemented in a FEM code and successfully applied to pull-out tests.

Chong Z., Yue T., Yao Q., Li X., Zheng C., Xia Z., Li H.

Rock reinforcement design necessitates a clear understanding of the initiation and propagation of cracks in the bolting system. To better understand the mechanism, we performed laboratory pull-out tests on resin-encapsulated rock bolts. Numerical models on a 1:1 scale were built using the discrete element method. The microscopic parameters of the model were calibrated based on unconfined compression tests and ring shear tests. The model allows us to visualize the progressive failure of a bolting system strengthened with resin-encapsulated rock bolts and elucidates the role of the anchorage length in controlling crack propagation. Comparisons indicate that the physical and numerical results are consistent. The results show that increasing the anchorage length improves the bondability and strength of the bolting system and restrains the complete debonding of the rock bolt from the cement mortar. At the same time, it also facilitates the conversion of shear cracks to tensile cracks. However, the shear crack of the resin is the dominant effect in the bolting system. In addition, the results reveal how factors such as boundary confining pressure, resin thickness, and cement-mortar strength affect crack initiation and propagation.

Jin-feng Z., Peng-hao Z.

The dynamic evolution characteristic of the bond strength at the interface of a bolt and a rock mass under an axial tensile load and the mechanical behavior of fully grouted bolts in situ were investigated considering the non-uniform stress of the surrounding rock along the bolts. A new dynamic bond-slip model was first proposed to describe the dynamic evolution characteristic of the bond strength at bolt-rock interfaces. Based on the proposed dynamic bond-slip model, analytical solutions of the shear stress distribution along the bolts, load-displacement relationship, and relative displacement considering the slip of the free end were developed. Then, incorporating the non-uniform normal stress of the surrounding rock along the bolts, the shear stress distribution and load-displacement behavior of the fully grouted bolts were presented. Moreover, analytical approaches were also proposed for determining the stress distribution along the bolt and rock deformation in cases of in situ prestressed and non-prestressed bolts. The proposed model and analytical solution were validated by published results from laboratory model tests and in situ tests , respectively. The new analytical solution completes the theoretical framework for addressing the fundamental problem of fully grouted bolts in pull-out tests and in situ rock masses and provides a useful theoretical tool that can potentially be applied to bolt design and laboratory and in situ testing .

Yan S., Song Y., Bai J., Elmo D.

Resin end-anchored rockbolts consist of three parts: (1) anchored section; (2) free section; and (3) faceplate and locking nut. Tensile failure of the bolt rod usually occurs in the free section. This paper presents a new model for end-anchored rockbolts loaded in tension by implementing a novel tensile failure criterion as part of a 3D continuum numerical modeling package. The proposed model is applied to the study of the behavior of end-anchored rockbolts in a deep coal roadway. The results are in close agreement with both experimental results and field observations in terms of load–displacement relationships and deformation characteristics. The results indicate that the use of rockbolts with high tensile strength and capable to undergo higher elongation would be a key controlling factor for designing excavations in deep coal mines, and the allowable elongation of the bolts in the ribs should be larger than the ones in the roof for deep coal roadways.

Xia N., Liang R.Y., Payer J., Patnaik A.

Developing predictive models for quantitative assessment of the deterioration of rock bolts exposed to corrosive environments is essential for rational planning of maintenance activities for anchorage structures. This article presents a probability-based computational model for predicting the time-dependent deterioration of bond capacity of corroding rock bolts due to the attack of chlorides. The inherent stochastic nature involved in the corrosion and degradation process is identified and simulated. A method is developed based on fundamental Mohr–Coulomb theory to evaluate the effect of corrosion on the bond strength due to a failure mode involving splitting of grout cover. Parameters affecting both strength and stress state at the bolt–grout interface are quantitatively related to the degree of corrosion. Integrating the realised corrosion stochastic process and the developed bond loss evaluation method, a computational algorithm based on Monte Carlo simulation is presented for evaluating the bond deter...

Kim N., Park J., Kim S.

A procedure of finite-element modeling and beam-column modeling of ground anchors was proposed in this study to investigate the load transfer mechanism in ground anchors. The procedure included the modeling of soil, grout, and strand tendon and the interface modeling of soil–grout and grout–strand in ground anchors. A series of finite element analyses and beam-column analyses were performed using the proposed models on ground anchors. The numerical predictions were compared with observed measurements in a field load test. The results indicated that the numerical simulation of load transfer mechanism on ground anchors can provide reasonable predictions.

Huang Z., Broch E., Lu M.

For stabilizing of rock cavern roof arches, tensioned rockbolts should be used with caution since they may have a negative influence on the stability of the arch. A proper design of rockbolts should therefore be based on a clear understanding of both the features of rockbolt reinforcement and the mechanism of the rock roof arch structure. For this purpose the mechanism of a rock cavern roof arch is studied and effects of different types of rockbolts are evaluated. Numerical modeling of rockbolt support of the Xiaolangdi powerhouse cavern as well as application of arching theory are carried out with the objective to study the effects of fully grouted rockbolts and tensioned cable anchors in reinforcing the cavern roof and walls, and on the forming of the roof arch.

Wang Y., Yin J., Lee C.F.

This paper presents a method that incorporates a non-associated flow rule into the limit analysis to investigate the influence of the dilatancy angle on the factor of safety for the slope stability analysis. The proposed method retain's the advantage of the upper bound method, which is simple and has no stress involvement in the calculation of the energy dissipation and the factor of safety. Copyright © 2001 John Wiley & Sons, Ltd.

Mindlin R.D.

A solution of the three-dimensional elasticity equations for a homogeneous isotropic solid is given for the case of a concentrated force acting in the interior of a semi-infinite solid. This represents the fundamental solution having a singular point in a solid bounded by a plane. From it may be derived, by a known method of synthesis, the solutions for the semi-infinite solid which correspond to the solutions known as nuclei of strain in the solid of indefinite extent.