Voussoir Beam Research Articles

Determination of the reasonable support working resistance

Support working resistance, as an important basis on choosing support, although has many determination methods, all of them have shortages due to lots of complicated influencing factors. Based on extensive reference on relative material of both home and abroad and according to the rock strata control theory, this paper compare support working resistance required in large height mining with that in slicing mining under the same geological condition by using theoretical analysis and field measurement, and successfully explains why the working resistance identified by the commonly 4-8 times High-density method in the large height mining is often lower. That is, the block can not meet the condition of voussoir beam but form cantilever beam, resulting in the roof-hanging distance is equivalent to the periodic weighting distance instead of roof-control distance. On this basis a new method called model method, which establish different mechanical models according to different geological condition, is put forward. The research results have been successful applied in Shendong mining area.

Investigations into stress shell characteristics of surrounding rock in fully mechanized top-coal caving face

A key issue in underground mining is to understand and master the evolving patterns of stress induced by mining, and to control and utilize the action of rock pressure. Numerical and physical modeling tests have been carried out to investigate the distribution patterns of stress in the rock surrounding a fully mechanized top-coal caving (FMTC) face. The results showed that a macro-stress shell composed of high stress exists in the rock surrounding an FMTC face. The stress of the shell is higher than its internal and external stress and the stresses at its skewback producing abutment pressure for the surrounding rock. The stress shell lies in the virgin coal and rock mass in the vicinity of the face and its sagging zone. The stress shell, which bears and transfers the loads of overlying strata, acts as the primary supporting system of forces, and is the corpus of characterizing three-dimensional and macro-rock pressure distribution of mining face. Its external and internal shape changes with the variations in the working face structure as the face advances. Within the low-stress zone inside the stress shell, another structure, i.e. voussoir beam, which only bears parts of the load from the lower-lying strata, will produce periodic pressures on the face instead of great dynamic pressure even if the beam ruptures and loses stability. The results show that the FMTC face is situated within the lower-stress zone, which is protected by the stress shell of the overlying surrounding rock. We give an explanation of lower occurrence of rock pressure on FMTC faces, and reveal the mechanical nature of the top coal of an FMTC face acting as a “cushion”. The strata behaviors of the face and its neighboring gates are under control of the stress shell. Drastic rock pressure in mine may occur when the balance of the stress shell is destruction or the forces system of the stress shell transfers.

Modeling mechanical layering effects on stability of underground openings in jointed sedimentary rocks

This paper examines the significance of mechanical layering for “blocky” rock mass deformation around underground openings excavated through sedimentary rocks. The analysis is based on an integration of geologically based discrete fracture models (“geoDFN”), which incorporate “mechanical layering”, with the numerical discrete element method—the discontinuous deformation analysis (DDA). We begin with addressing limitations of classical solutions for mine roof stability in layered and jointed rock masses via the analysis of the free standing, unsupported, 2000-year-old underground quarry known as Zedekiah's cave below the old city of Jerusalem, Israel. We show that both the “clamped beam” model and the “Voussoir beam analogue” fail to predict the observed roof stability. Only application of discrete element modeling, which allows for interactions between multiple blocks in the rock mass, can capture correctly the arching mechanism which takes place in the roof and which properly explains the long-term stability of this underground opening. We continue with examining the effect of joint trace geometries on “blocky” rock mass deformation using the hybrid geoDFN-DDA approach. We show that with increasing joint length and decreasing bridge length vertical deformations in the rock mass are enhanced. We explain this by the greater number of distinct blocks in the rock mass due to the greater joint intersection probability in such geometries. We find that rock bridge length is particularly important when considering the stability of the immediate roof. With increasing rock bridge length the number of blocks in immediate roof decreases and consequently individual block width is increased. Increased block width in immediate roof layers enhances stable arching development, thus improving their load carrying capacity and overall stability of the underground structure.

Geomechanics stability assessment of World War I military excavations at the Canadian National Vimy Memorial Site, France

The Canadian National Memorial Site, Vimy Ridge, France, commemorates the efforts and loss of life of Canadian troops in the First World War (WWI). The site comprises the monument, a Visitors Centre, the Grange Tunnels and restored trenches and several cemeteries. A substantial portion of the battlefield terrain remaining from WWI is preserved at this site, including trenches, shell holes and military mining craters. The ground surface is further disturbed by subsidence of the ground surface into underground excavations left from the war. A significant number of subsidence events have been recorded within the last decade. There is concern that ground surface subsidence could compromise the safety of visitors or workers at the site. The excavations of concern include dugouts, headquarters and hospitals, and were excavated in chalk. Possible excavation types, dimensions and support were investigated in the historical literature. To assess the potential for ground subsidence, the geological setting was investigated and the chalk was mapped and sampled, to determine the geomechanical characteristics of the material. The chalk was accessed in quarry excavations and in tunnels and declines that have been discovered and re-opened in recent years. Finally, the influence of excavation geometry and depth, chalk condition and effects of weathering on the excavation stability were assessed using numerical simulation, using a finite element program, and considering voussoir beam stability. Interpretation of the results of this analysis allow development of general relationships between span, depth and possible failure to isolate excavation classes that pose a long-term hazard, and to reduce the priority for those that are unlikely to fail to surface as well as those that are likely to have failed soon after construction.

Modeling of a Multiply Jointed Voussoir Beam in the Centrifuge

The mechanics and kinematics of a multiply jointed Voussoir beam have been studied based on the response of small scale beams tested in the centrifuge. The model beams were made up of six blocks, confined between fixed abutments. The tests included monitoring of beam deflection, development of axial thrust and distribution of strain within the beam. The models were subjected to accelerations of up to 90 g, depending upon the beam geometry. Two different beam geometries were considered.

Geotechnical studies and optimal slope design at Lajkura opencast coal mine, India

Dynamic loading events in the longwall faces under slopes in the Shendong Coalfield, China, seriously limit the safety and efficiency of mining. The slope characteristics, such as direction, height, and angle, determine the load type and the stability of the voussoir beam structure (VBS) formed by fractured blocks of the primary key stratum (PKS). Whether or not dynamic loading events will occur can be directly determined based on the presence or absence of a stable VBS in the PKS. Based on this relationship, six structural mechanical VBS models for different load distributions were established and then the effects of the slope direction, height, and angle on the stability of VBS was analysed. Changes of load type intensified the compression force between the hinged blocks. When the compression force between blocks exceeded the strength of the rock, VBS instability and dynamic loading events occurred. The compression force in the VBS increased with increasing slope angle and height when the slope directions were similar, becoming more pronounced for mining under the uphill sections of the slopes. Therefore, a method of determining the critical slope parameter values indicating a risk of dynamic loading was proposed, enabling such slopes to be recognised in advance. Measures such as slope top cutting or backfilling can then be applied to prevent potential dynamic loading accidents. This study can provide guidelines for safe mining under geological conditions involving widespread slopes and gullies.

Geotechnical sedimentology—its use in underground coal mining

From a geotechnical perspective, bedding is a discontinuity in a rock mass. Sedimentology is concerned, in part, with the origin of bedding. There is much to be gained by a melding of the two disciplines in the underground coal-mining sector. Bedding controls the strength of rock units in coal measures by defining beams that may or may not span openings. Voussoir beam theory can be used to explain how massive sandstone/conglomerate units can span longwall panels and what thickness of roof beam is required to span a coal mine roadway. Bedding also controls the way in which stresses are distributed about coal mine openings. By utilizing transverse isotropic elastic properties, the effect of bedding can be readily implemented in continuum numerical codes. Geologists logging core need to discriminate between bedding as a textural element in the rock and bedding as a geotechnical discontinuity. Geotechnical engineers need to explicitly consider bedding when formulating their design models.

Stability of large excavations in laminated hard rock masses: the voussoir analogue revisited

The voussoir beam analogue has provided a useful stability assessment tool for more than 55 years and has seen numerous improvements and revisions over the years. In this paper, a simplified and robust iterative algorithm is presented for this model. This approach includes an improved assumption for internal compression arch geometry, simplified displacement determination, support pressure and surcharge analysis and a corrected stabilizing moment in the two dimensional case. A discrete element simulation is used to verify these enhancements and to confirm traditional assumptions inherent in the model. In the case of beam snap-through failure, dominant in hard rock excavations of moderately large span, design criteria are traditionally based on a stability limit which represents an upper bound for stable span estimates. A deflection threshold has been identified and verified through field evidence, which corresponds to the onset of non-linear deformation behaviour and therefore, of initial instability. This threshold is proposed as a more reasonable stability limit for this failure mode in rockmasses and particularly for data limited cases. Design charts, based on this linearity limit for unsupported stability of jointed rock beams, are presented here summarizing critical span–thickness–modulus relationships.

Tensile strength and abutment relaxation as failure control mechanisms in underground excavations

Classical assessment of instability potential in underground excavations are normally based on yield and rupture criteria for stress driven failure and on limit equilibrium analysis of structurally controlled failure. While it is true that ultimate failure and falls of ground can be an eventual consequence of stress fracturing and unfavourable structure within the rock mass, the timing of such failure is often controlled by the presence of residual tensile capacity, in the form of rock bridges separating joint segments and fractures and by the mechanisms of clamping and relaxation. Using crack and rock-bridge analogues in conjunction with an updated voussoir beam model, this paper explores the influence of residual tensile strength and boundary parallel relaxation on the failure process. The impact on support design is also examined. In underground hard rock mines with complex geometries and interacting openings, relaxation is identified as a key controlling factor in groundfall occurrence. Empirical stability assessment techniques for underground tunnels and for mining stopes are updated to account for relaxation.

Numerical evaluation of the response in bending of an underground hard rock voussoir beam roof

The behaviour of a hard rock horizontally stratified roof, within a low primary lateral stress field, is investigated. The lowest roof stratum is modelled as a voussoir beam with three cracks, one at the midspan and one at each abutment. Its response in bending is computed, with the help of a distinct element computer code, for an ordered series of configurations. Two states of failure, i.e. buckling and crushing, are examined. The parameters of indeterminacy of the structure are investigated numerically and improved relations are derived for their evaluation. From the solution of the determined structure, deflections, strains and stability limits are evaluated analytically and validated numerically. Finally, in order to check against crushing, a chart is provided for the prediction of the lateral non-linearly distributed axial strain at the extreme fibre of the abutment.

The stability of a laminated Voussoir beam: Back analysis of a historic roof collapse using DDA

The stability of a horizontally bedded and vertically jointed roof, referred to here as a laminated Voussoir beam, is studied using careful documentation of a historic roof collapse, which occurred in an ancient underground water storage reservoir dated back to ca. 1000 B.C. The roof of the opening failed immediately after the excavation leaving a dome shaped loosened zone, with a span of 7 m and height of 2.5 m, consisting of horizontal beds and vertical joints with mean spacing of 50 and 25 cm, respectively. The ancient engineers erected a massive pillar at the center of the dome in order to passively support the failed roof and the opening remained in service for several hundred years following the failure. Analysis of the roof using iterative Voussoir beam procedure [Beer, G. and Meek, J. L., Design curves for roofs and hanging walls in bedded rock based on Voussoir beam and plate solutions. Trans. Inst. Min. Metall. , 1982, 91 , A18–22.] shows that the roof was more sensitive to failure by shear along the abutments rather than by crushing at hinge zones and that the required friction angle ( φ req. ) for stability would have been 36°. The available friction angle is estimated between 38.6° and 46.4° and, therefore, the result of the iterative solution is considered unconservatively wrong. Results of DDA [Shi, G. -H. and Goodman, R. E., Two-dimensional discontinuous deformation analysis . Int. J. Numer. Anal. Methods Geomech. , 1989, 13 , 359–380; Shi, G. -H., Block System Modeling by Discontinuous Deformation Analysis . Computational Mechanics Publications, Southampton, 1993, pp. 209.] however indicate that φ req. must have been greater than 60°, a shear strength which was not available at the time of construction, thus the immediate failure. Using DDA we further demonstrate that φ req. is related to joint spacing (or block length) in a parabolic function: with increasing joint spacing φ req. decreases to a minimum value and than increases with further increase in joint spacing. This result is attributed to the interaction of two competing forces: one is the stabilizing axial thrust which increases with increasing moment arm in individual blocks (a function of joint spacing or block length), the other is the destabilizing vertical load which increases with increasing weight of overlying blocks.

Editorial

In this paper, the discontinuous deformation analysis (DDA) is applied to numerically investigate the formation of pressure arch and the stabilization mechanism of rock bolts for underground excavation in laminated rock mass. A global pressure arch with elevated stress is observed sustaining the weight of the overburden and providing the natural shield over the opening. Below the pressure arch is a loosened zone, where a group of local voussoir beam arches are formed to transfer the weight of each layer to the abutments. Detailed parametric studies regarding the in-situ stress ratio, joint friction angle, overburden depth and dip angle of strata are conducted and their influences on the formation of global pressure arch and local voussoir beam arches are identified and discussed. Based on the observed phenomena, the corresponding reinforcement scheme is proposed and the effectiveness and stabilization mechanism are examined.

Analysis and design of an underground hard rock voussoir beam roof: A. I. Sofianos, International Journal of Rock Mechanics & Mining Sciences, 33(2), 1996, pp 153–166

Analysis and design of an underground hard rock voussoir beam roof: A. I. Sofianos, International Journal of Rock Mechanics & Mining Sciences, 33(2), 1996, pp 153–166

Design of the jointed roof in stratified rock based on the voussoir beam mechanism : P. Mottahed & J. Ran, CIM Bulletin, 88(994), 1995, pp 56–62

Mining practice and research have shown that the jointed roof in stratified rock behaves like voussoir beam structure with strength greater than that determined by the continuous beam theory. Previous studies have demonstrated the voussoir beam mechanism and developed methods to estimate the crushing and buckling strength of voussoir beams. However, research on voussoir beams with multiple mid joints has not been sufficient and problems such as the voussoir beam support and applications of the voussoir beam mechanism to the mining environment have not been addressed. In this paper, mechanism of voussoir beams containing multiple mid joints and truss support are studied and applications of the voussoir beam mechanism to underground mine openings are discussed based on the numerical and experimental results.

Analysis and design of an underground hard rock voussoir beam roof

The behaviour of a voussoir hard rock beam roof is investigated by considering it to act as a symmetric flat arch with cracks at the abutments and at midspan. Analytical formulae are derived initially that evaluate, for any given geometry, loading and mechanical parameters of the beam, its deflection and strain within it in terms of the extreme and mean arch thickness. The latter are determined statistically by best fitting a large amount of available computer beam model responses. Three relations are then established, one for each of the three examined modes of failure, i.e. snap through, crushing of the rock and transverse slip at the abutment, that relate the loading of the beam, its mechanical parameters and its dimensions. Finally all three relations are incorporated in a single non-dimensional graph where the loading and the mechanical parameters of the beam are related to the geometry of the beam for various factors of safety of the three modes of failure.

Analysis of key block in the structure of voussoir beam in longwall mining (in Chinese) : Qian Minggao, Miao Xiexing & He Fulian, Journal - China Coal Society, 19(6), 1994, pp 557–563

Analysis of key block in the structure of voussoir beam in longwall mining (in Chinese) : Qian Minggao, Miao Xiexing & He Fulian, Journal - China Coal Society, 19(6), 1994, pp 557–563

Shear sliding failure of the jointed roof in laminated rock mass

The jointed roof in laminated rock mass may be capable of self-support and sustaining transverse load and can be analysed by the voussoir beam notation. There are three main failure modes of a voussoir beam structure: crushing in the high stress areas, buckling without localised material failure and shear sliding along the joints. Previous studies on the voussoir beam have concentrated on the crushing failure mode, assuming that the voussoir beam would not fail by shear sliding prior to reaching its crushing strength. However, the possibility exists that the voussoir beam may collapse by shear sliding along the joints with a strength much lower than that predicted by the estimation method for crushing failure, depending upon the joint properties. Hence the stability analysis of a jointed roof without considering the shear sliding failure may lead to disastrous consequences. In this paper a numerical and experimental study has been carried out to analyse the shear sliding failure of voussoir beams containing vertical and inclined joints with one or more mid joints. Equations for verification of shear sliding are proposed and effects of the voussoir beam geometry and material properties on the shear sliding failure are also discussed.

Stability of the jointed roof in stratified rock

In this paper, a finite element program that can simulate non-linear joints and geometry non-linearity was developed and a large scale test rig was used to study the mechanism of the voussoir beam. The deformation and failure mechanism are analysed and equations and methods for strength estimation are proposed. Furthermore, the effects of multiple mid joints and applications to the stability analysis of a jointed roof are presented. (A) This paper was presented at the 34th U.S. Symposium on rock mechanics, 27-30 June 1993, University of Wisconsin-Madison. For the covering abstract see IRRD 863389.

Back-analysis of roof conditions in the Great Northern SEam, Newcastle coal measures, Australia, using voussoir beam theory : Seedsman, R Int J Min Geol EngngV5, N1, March 1987, P15–27

Back-analysis of roof conditions in the Great Northern SEam, Newcastle coal measures, Australia, using voussoir beam theory : Seedsman, R Int J Min Geol EngngV5, N1, March 1987, P15–27

Back-analysis of roof conditions in the Great Northern Seam, Newcastle Coal Measures, Australia, using voussoir beam theory

A typical roof profile for mine openings in the Great Northern Seam consists of a thin coal layer and several metres of claystone. From field evidence and shear flow analysis, the anchorage of fully grouted roof bolts in the claystone may fail. If so, the claystone may act as an extra load on the coal beam. Using voussoir beam theory, the relation between the minimum thickness of the coal beam, the thickness of the failed claystone and the width of the entry has been determined. The analysis is satisfactory for field performance observed in a number of case studies. Proposals are made on possible improvements to mining techniques.