Composite element method for the bolted discontinuous rock masses and its application

doi:10.1016/j.ijrmms.2007.07.002

International Journal of Rock Mechanics and Mining Sciences

Volume 45, Issue 3, March 2008, Pages 384-396

https://doi.org/10.1016/j.ijrmms.2007.07.002 Get rights and content

Abstract

This paper presents a composite element method (CEM) for discontinuous rock masses reinforced by fully grouted bolts. This element allows one to generate mesh without considering exactly the existence of bolts and joints, which further allows for an important simplification in the pre-process work. The sub-elements of rock, grout, bolt, joint, rock/grout interface and bolt/grout interface are defined using corresponding mapped nodal displacements at the composite element. The mapped nodal displacements can be determined using the governing equations established by means of the virtual work principle. Based on the mapped nodal displacements deformation and stress in each sub-element can be further obtained. The comparative study of the CEM and the conventional finite element method (FEM) has been carried out for the preliminary verification example. The numerical study for the rock bolt crane girder of an underground powerhouse by FEM and CEM is presented as the engineering application example, in which the attention has been paid to the portion of the contact face between the girder and surrounding rock masses, the contact faces between the bolts and surrounding rock masses, as well as to the portion where the rock bolt penetrates the contact face. The comparative and application studies show the validation and advantages of the CEM.

Introduction

The stabilization of rock masses by bolts is widely used in excavation and foundation engineering. The use of bolts allows an increase in the shear resistance along the joints, which is expressed in three parts: tension force in the bolt, friction as a consequence of the increase in the normal stress, and dowel effect.

Numerical simulation of bolts and joints can be implemented by the explicit (or distinct) modelling method [1], [2], [3], [4]. It can also be implemented using the implicit (or equivalent) modelling method [5], [6], [7], [8], [9]. The first method allows one to describe the bolt's behaviour in more detail, while the second one can be applied in complicated engineering problems with a large number of joints and bolts.

In order to combine the advantages of both the explicit and the implicit methods, the composite element method (CEM) is proposed for rock bolts [10] and rock joints [11], respectively. The peculiarities of the CEM are that CE mesh is a combination of the joint or bolt system and the conventional FE mesh which is generated mainly according to the structure configuration and the stress gradient. A composite element contains several sub-elements defined by joint or bolt segments. The displacement within each sub-element is interpolated from the corresponding nodal displacements. The CEM can be integrated easily into the finite element method (FEM) algorithm.

This paper presents an important extension of the CEM for the rock masses with both joint and bolt segments. Consequently, the effect of a bolt on its intersection with a joint can be considered. This issue is important in the study of the jointed rock masses reinforced by bolts. The validation and advantages of the proposed method is verified through the comparative study and application study.

Section snippets

Solid material sub-elements

The FE mesh should be generated to discrete the rock engineering structure firstly. The deployment and sizes of the finite elements are dependent on the structure configuration and stress gradient. Then the presence of joints and bolts is considered by the transformation of some finite elements into composite elements. Fig. 1 shows a composite element containing one joint segment and one bolt segment, respectively. This element is composed of two rock material sub-elements separated by the

Composite element analysis

Suppose the virtual displacements at the composite element are $({U})^{*} = [({U}_{r_{1}})^{*}, ({U}_{r_{2}})^{*}, ({U}_{g_{1}})^{*}, ({U}_{g_{2}})^{*}, ({U}_{b_{1}})^{*}, ({U}_{b_{2}})^{*}]^{T},$ then the corresponding virtual displacements and virtual strains within the sub-elements can be calculated according to Eqs. (1), (3), (9), (11), (15).

The application of the virtual work principle to the composite element leads to the following expression: $W_{r_{1}} + W_{r_{2}} + W_{g_{1}} + W_{g_{2}} + W_{b_{1}} + W_{b_{2}} + W_{j_{r_{l} r_{m}}} + W_{j_{g_{1} g_{m}}} + W_{J_{b_{l} b_{m}}} + W_{J_{r_{1} g_{1}}} + W_{j_{g_{1} b_{1}}} + W_{j_{r_{2} g_{2}}} + W_{j_{g_{2} b_{2}}} = ({U}_{r_{1}})^{* T} {f}_{r_{1}} + ({U}_{r_{2}})^{* T} {f}_{r_{2}} + ({U}_{g_{1}})^{* T} {f}_{g}$

Verification

The verification of the CEM is carried out on the rock block (5 m×5 m×5 m) illustrated in Fig. 6. The block contains a horizontal joint and a vertical bolt from the top center. The bolt is 3 m in length, the radii of the bolt and the grout are 20 and 38 mm, respectively. Table 1 summarizes the parameters used in the calculation.

The FEM and CEM are carried out for the vertical pull-out test (pull-out force P=100 kN acting at the top of the bolt, Fig. 6a) and the direct shear test (the shear force P=20

Presentation of the project

The size of the underground powerhouse of Ximahe Project is 74.4 m×17.4 m×37.6 m (length×width×height), the size of the transmission cavern is 58.42 m×13.6 m×25.55 m (length×width×height). The surrounding rock mass is layered limestone. The overburden rock above the power house is 120–160 m. The rock bolt crane girder is used to support the crane.

The excavation of the powerhouse is divided into six steps, as shown in the Fig. 10. The excavation and reinforcement procedure is shown in Table 2. ∅25

Conclusions

This paper presents a composite element method (CEM) for the discontinuous rock masses reinforced by fully -grouted bolts. This composite element includes the sub-elements representing rock, grout, bolt, joint and interfaces. The displacements within these sub-elements are calculated by the corresponding nodal displacements mapped on the composite element.

The CEM provides a detailed description of the bolt's behaviour at the joint as well as the bolt's interaction with rock and grout using

Acknowledgements

Support of the National Science Foundation of China (NSFC: 50679066, 50639090) is gratefully appreciated. The authors thank the Lille University of Science and Technology who offered a guest professor position for the first author to complete this research in 2006–2007.

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Composite element method for the bolted discontinuous rock masses and its application

Abstract

Introduction

Section snippets

Solid material sub-elements

Composite element analysis

Verification

Presentation of the project

Conclusions

Acknowledgements

Int J Rock Mech Min Sci Geomech Abstr

Int J Rock Mech Min Sci Geomech Abstr

FEM modelling of rockbolts

Numerical modelling of rock bolts in intersection with fault system

Elasto-viscoplastic distinct modelling of bolt in jointed rock masses

Bolt action in jointed rock