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By Eric R. Bauer

Skin failures of roof and rib in underground coal mines continue to be a significant safety hazard for mine workers. Skin failures do not usually involve failure of the support systems but result from rock or coal spalling from between the support elements. For instance in 1997, over 800 miners were injured by roof and rib falls, of which 98 pet were the result of skin failures. Also, nearly 80 pct of the roof and rib failure injuries occurred at or near the working faces in development sections. The face area is a zone where the potential for skin failure accidents and injuries and roof and rib failures, in general, is high because of mining activity, ground readjustment due to changing stress conditions, and the higher exposure of mine workers. In addition, failures occur where the roof and rib are unsupported. This paper features a review of the roof and rib accident statistics resulting from skin failure, highlighting the incidences by average days lost, in-mine location, state, MSHA District, and worker activity at the time of injury. A detailed analysis of recent fatalities caused by skin failure is included. Also discussed are the causes of roof and rib skin failures, current methods and support materials for skin surface control, as well as a historical literature review of skin failures and control methods.

Jan 1, 1999

By Yanfa Gao

Abstract In order to control and reduce ground subsidence due to coal mining, and to protect building, railway and other surface construction, a new subsidence control method is proposed. Ground subsidence is reduced by grouting bed separations in overlying strata with fine-coal ash. Engineering application tests have been performed for 5 years in Tangshan Coal Mine. Kailuan Group Corporation. China. The technology has been applied to 4 fully mechanized sublevel caving mining faces. Its effect in reducing subsidence has been significant. The technology including grouting engineering design method and ground subsidence prediction theory is introduced in detail. Keywords: overlying strata separation, multi-layer grouting, subsidence control

Jan 1, 2002

By Daniel W. H. Su

Thick, massive sandstone present in close proximity of the mining horizon can create difficult longwall caving issues, which may lead to severe face loading and subsequent face roof control problems. Under deep cover, such delayed caving and overhang not only impose additional loading on the gate road pillar system, but they also increase the potential for large seismic events. Such a combination of thick, massive sandstone geology and deep cover was present over a portion of a southwestern Virginia coal mine, which was confirmed via detailed in-mine roof scoping and mapping. Large seismic events were recorded over a district of 1,000-foot-wide longwall panels. This paper presents the ground control design changes implemented to reduce longwall-induced stresses in the sandstone, to reduce longwall abutment pressures in the gate road pillars, and to reduce the magnitude of mining-induced seismic events. A series of two-dimensional finite element models were constructed and analyzed to evaluate the longwall-induced stresses in the sandstone above the gate road pillars and the abutment pressures within the gate road pillars. Results from the analyses indicated that reducing the panel width from 1,000 to 700 feet reduced the longwall-induced stresses in the sandstone by a factor of 2.0. Specifically the probability of sandstone stability improved from 29% for the 1,000-foot-wide panel district to over 95% for the 700-foot-wide panel districts. Also, the subcritical 700-foot-wide panel, coupled with a change in pillar design, considerably reduced the longwall-induced abutment pressures in the gate road pillars, which significantly increased the gate road pillar stability factor. Surface subsidence measurements conducted over the 1,000-foot-wide panel district and two new 700-foot-wide panel districts were in very good agreement with those predicted by the finite element models. In addition, results from the models indicated that wider panels with a smaller district may produce the same probability of sandstone stability. One four-panel district and one five-panel district with the new ground control design changes have been mined successfully. The panel width was found to be the most influential factor in determining the longwall-induced stresses in the sandstone and in the gate road pillars. The thickness and massive nature of the sandstone, the proximity of the sandstone, and the strength of the sandstone were also found to be important factors. Seismic monitoring over the two mining districts that employed 700-foot-wide panels confirmed the reduction of one order of seismic magnitude when compared with those measured over the 1,000-foot-wide panel district.

Jan 1, 2014

By George Gardner

The rapid growth of highwall mining in the Appalachian coalfields has resulted in unique safety concerns. Due to the concentration of activity at the base of the highwall and the potentially destabilizing influence of the mining process, proper mine planning and continual monitoring of the ground conditions is essential to ensure a safe and productive operation. This will also help to minimize the need to recover equipment that has become entrapped underground, and the subsequent hazards associated with a recovery operation. Adequate geotechnical site investigation and rational design methods should enable mine planners to properly account for the site-specific conditions that influence web and abutment pillar, roof, floor, and highwall stability. This paper examines the growth of highwall mining, provides a general overview of the various safety concerns, and reviews the modes of highwall failure as they relate to a highwall mining operation. Gcotechnical considerations that should be taken into account before and throughout the mining operation are emphasized. The importance of closely examining and monitoring highwall conditions for subtle signs of highwall instability will be discussed.

Jan 1, 2002

By Timothy Batchler

"Standing roof supports help to provide a stable working environment in coal mine gateroads. NIOSH participates in the development of these support systems by conducting full-scale tests in their Mine Roof Simulator. These tests have established the performance characteristics of every coal mine support system currently in use in the United States. Through these tests, mine operators and regulatory officials have acquired a fundamental understanding of the various types of support performance that guides the assessment and use of these support systems. However, some little known factors that influence support behavior can lead to misconceptions and, perhaps, a poor assessment of support behavior at times. This paper highlights several of these factors and discusses their significance. The paper also examines a current longwall tailgate support and discusses the inefficiency with this approach. Finally, the NIOSH Mine Roof Simulator (MRS) is the world’s most powerful load frame built specifically to test full-scale roof supports, including longwall shields. are addressed in this paper to provide a more in-depth assessment of the limitations of the MRS and what the MRS testing protocol is designed to do. INTRODUCTION Over the years, considerable research has been conducted to develop standing support technologies and to evaluate their performance characteristics. The load and displacement characteristics of the standing supports have been determined from full-scale testing conducted using the National Institute for Occupational Safety and Health (NIOSH) Mine Roof Simulator (MRS) (Barczak and Tadolini, 2008) located in Bruceton, PA. Performance traits, installation patterns, and ground responses are observed in various geological and mining conditions and are evaluated to determine the support performance in the field (Dolinar, 2010; Campoli, 2015; Zhang et al., 2012). Despite widespread use of standing supports, not every aspect of their performance and resulting ground support capability are always well understood. This paper discusses 10 factors, several of which are surprising, that impact standing support performance."

Jan 1, 2017

By Joseph Hirschi, Naga S. Y. Tirumalaraju, Aditya Mishra, Anthony (Sam) J. S. Spearing

"Primary roof support in underground coal mines in the USA consists mostly of fully grouted passive rebar or grouted (partially or fully) tensioned rebar. Research conducted at two room-and pillar coal mines in the Illinois Basin and one longwall mine in Colorado monitored the performance of these passive and active rock bolts under similar geologic and mining conditions and found no significant initial loads in either passive or active rock bolts (Spearing et al., 2011). Active rock bolts showed significant loss of initial pre-load, although the exact reasons for this were not fully investigated. Subsequent laboratory testing has also shown that in weak rock, resin creep occurs, caused by slippage of the mechanical key between resin column and rock interface. These creep tests were studied in the laboratory in an effort to quantifythis phenomenon.INTRODUCTIONResin-grouted rock bolts are the first and main line of defense to counter roof and rib falls in underground coal mines of the United States. Rock bolts are categorized as active or passive. Active bolts are tensioned during installation whilst no (or limited) tension is applied to passive bolts, which need subsequent strata movement to generate reactive loads. During installation of passive bolts, some reactive pre-load may be generated by a significant up-thrust from the rock bolter boom.The selection of active or passive bolts is critical and is mostly dependent on the conditions and properties of the immediate roof (Unrug, 2009). This decision is frequently made based on personal experience, bias, and most recently cost. Active bolts are generally used in cases of highly laminated roof rock. When active bolts are tensioned, they develop compressive forces between these layers forming a beam, which helps to stabilize weak individual layers thereby increasing frictional forces between layers and decreasing effects of horizontal stresses. The fully grouted tensioned rebar system is high in stiffness as compared to mechanical bolts and provides higher surface area of contact along the length of the bolt due to the grout, which permits it to develop a strong anchorage mechanism."

Jan 1, 2015

By Arthur Miller, Andrew Weakley, Heather E. Lawson

"IntroductionDynamic failure events in an underground coal mine, or “bumps,” are defined as “the sudden, violent bursts of coal from a pillar or pillars or a block of coal, resulting in a section, the whole pillars, or the solid block of coal being thrown into an open entry” (Peng, 2008). Reports of disastrous and often fatal dynamic failure events date back over one hundred years in the United States. Mining practices and technologies have significantly evolved over the course of the last century, yet these events continue to occur. The events at Crandall Canyon, Utah (Gates et al., 2007) and Brody No. 1 Mine in West Virginia (Barker and McNeely, 2014) are two recent failure events that resulted in a total of eleven fatalities. These events testify to the fact that dynamic failure remains an imperative safety concern. Furthermore, their continued occurrences indicate that engineering controls have proven inadequate at wholly mitigating the problem.Multiple conditions have been associated with the occurrence of dynamic failure phenomena, including• thick, competent strata that can create a bridging effect, resulting in high abutment stresses (Rice, 1935; Holland and Thomas, 1954; Iannacchione and Zelanko, 1995; Agapito and Goodrich, 2000; Peng, 2008; Whyatt, 2008; Whyatt and Varley, 2010)• overburden thicknesses greater than 500–700 ft. (Rice, 1935; Peng, 2008)• a strong coal that is resistant to crushing (Rice, 1935; Peng,2008) or that is “uncleated or poorly cleated, strong…sustains high stress and tends to fail suddenly” (Agapito and Goodrich, 2000)• the presence of sandstone channels or rolls that can serve to concentrate stresses (Iannachione and Zelanko, 1995; Agapito and Goodrich, 2000)• fracturing of strong units above or below the coal seam (Whyatt and Varley, 2010)• slip along pre-existing discontinuities (Peperakis, 1958; Whyatt and Varley, 2010)• multiple seam mining interactions (Campoli, Kertis, and Goode, 1987; Iannachione and Zelanko, 1995; Newman, 2002; Peng, 2008)• mining sequences that can cause anomalously high stress concentrations (Campoli, Kertis, and Goode, 1987; Iannachione and Zelanko, 1995)"

Jan 1, 2015

By Reha Ozel

The stability in longwall faces depends on the interaction beman the roof strata, face supports and floor strata. The load distribution on the other hand, depends upon relative stiffness of the three supporting elements namely, the coal face, support and gob. Therefore, in defining support requirements, it is particularly important to analyze the strata loading, the face convergence and the controlling mechanism provided by supports. The controlling mechanism however, depends on the type and characteristics of supports used in long- wall faces. The design guidelines presented in this paper have bean developed based on a number of strata control oriented projects carried out in Turkey, load and convergence measurements carried out in 10 longwall faces, in Zonguldak Coal Region, and procedures given in literature. Evaluation of load and convergence measurements, and analyses of face supports were carried out by means of a computer program, called L0NGWAI.L-MEW, developed by the authors. The output of the design analyses include the following: (1) estimation of support capacity for roof supports namely; individual hydraulic props, chock-type power supports and various types of shield supports, and (2) analysis of loading conditions and response of shield support components in terms of stability and structural integrity.

Jan 1, 1990

By E. Bane Kroeger

Rib failure is a hazard that has resulted in many injuries and fatalities in underground coal mines, especially in soft coal seams. Conventional rib control methods including rib boarding, shotcreting. steel meshing and geogridding, are fairly expensive and time consuming to install. Some methods, such as rib boarding, have met with marginal success at controlling rib failure. Under this research, the Rib Strap System (RSS) introduced by Dr. Chugh in 1999, was modified and new components were added. Both bench scale and full size prototypes were tested in the labs at SIUC to determine the best materials for fabrication and easier methods for assembly and installation. This laboratory research has developed new methods of securing the strap ends to smaller rib hoards, a new device to post-tension two straps together, and a technique for replacing straps without having to drill new rib bolts or for retrofitting straps to rib hoards that are already in place. The method used to secure the strap end to rib boards developed during bench-scale testing was dubbed the wrapped staple technique. It is very simple, requiring only 10-15 staples, with the end of a strap secured to a rib board in about 45 seconds. Several different prototype designs for a new device to join the strap ends together and tension the strap were fabricated and tested in the labs at SIUC. The device, dubbed the rib strap buckle, was very easy to install and held the straps firmly. One specific buckle design worked extremely well during testing and exceeded all expectations. The laboratory research also developed a method of replacing a damaged rib strap that can also be used to add rib straps to existing rib boards. The technique uses nails, spacer blocks, and band clamps to secure the new board and strap. This technique was developed to allow one person to replace a strap using only a hammer and screwdriver, negating the need to drill and install a new rib bolt using mine equipment such as a roof bolter or scoop. In addition to the technical feasibility, the cost of materials for the rib strap system was compared to the rib boarding method currently being used at a mine in the Illinois Basin. The mine is using 20 rib boards on each pillar at cost of about $223.60. The costs for the rib strap system depend on the materials chosen for fabrication but for the base case, were about $97 per pillar.

Jan 1, 2004

By Gabriel S. Esterhuizen

The design of support for underground excavations is a complex process in which the interaction between supports and the rock mass must be evaluated. The strength reduction method (SRM) is useful because it provides a stability factor of the supported excavation that can easily be compared between support alternatives. The method is based on numerical model analysis where the stability factor is determined by reducing the rock mass strength until collapse is indicated in the model. This paper presents the results of validation studies that were conducted using the FLAC3D stress analysis software to compare SRMcalculated stability factors to the empirically based Coal Mine Roof Rating (CMRR) and the Analysis of Roof Bolt Systems (ARBS). The objective was to determine whether the SRM, with its basis in mechanics, would predict similar outcomes as the fundamentally different ARBS and CMRR methods with their basis in empirical observations. A total of 450 different scenarios were evaluated in which the geology, horizontal stress, depth of cover, entry width, support spacing, and support length were varied. The results showed that the SRM-calculated stability factors were able to satisfactorily capture both the ?weak bed? and ?strong bed? adjustments in the CMRR. The SRM results were found to be well correlated to the ARBS stability factors for the 450 cases considered. Further analysis showed that the SRM accurately captures the effect of bolt length, depth of cover, and entry width on the overall stability of an entry.

Jan 1, 2013

By Leslie Carver

The effects of longwall mine subsidence on water resources were studied at a West Virginia coal mine (mine Z) by Carver (1994). Data were obtained for 137 domestic supply wells and springs and 12 baseflow streams. Subsidence caused short-term dewatering (of a few days to weeks) of wells located on lower hillslopes and valleys, and long-term dewatering of hillslope and hilltop springs (with no recovery yet). New or increased spring discharge was observed at lower elevations. Unsubsided water supplies experienced no dewatering beyond a nearby panel's 27°-38° angle of dewatering influence zone. Subsidence from longwall mining beneath streams commonly reduced discharge when panel ages were less than two to three years. However, "normal" discharge was typically observed over panels greater than three years in age; such streams exhibited lower baseflow recession constants, moderated winter baseflow, and increased summer baseflow compared to unsubsided streams.

Jan 1, 1994

By Stephen C. Tadolini, John P. McDonnell

"High-strength cable bolts have been used for ground support in underground coal mines for many years. Cable bolts are routinely used as secondary ground support in numerous longwall gateroad support applications, areas that possibly experience the most severe conditions in current underground coal mining. Additionally, when mining ground conditions deteriorate, engineers oftentimes recommend cable supports as a principal solution because of the established credibility for successful ground control. Nevertheless, there is still a reluctance to utilize non-tensioned cable supports as an effective primary roof support alternative.This paper provides historical and recently documented examples of non-tensioned cable supports utilized as an effective primary ground support method in a western U.S. underground coal mine, and it will continue the technical discussion between the differences of various degrees of tension in cable supports with respect to ground behavior and reactions.INTRODUCTIONResin-grouted cable supports are widely used to support difficult ground conditions throughout the world. Through the use of innovative applications and configurations they have proven to be a major paradigm shift in roof support and ground control technology in the U.S. (Tadolini and Koch, 1993; McDonnell et al., 1995; Tadolini and Gallagher, 1994; Tadolini and Trackemas, 1994)Today, the basic cable bolt support consists of a high-strength steel cable installed in bore holes that range in diameter from 25 to 50 mm (1 to 2 in) depending on the strand size and drilling equipment. Cables are offered in both bright and galvanized, for corrosion protection, and range in capacity from about 30 to 60 tons. An example of a resin-grouted cable bolt and the key components is shown in Figure 1. The steel cables are flexible and the support length is not limited by the height of the opening. Lengths of up to 10 m (32 ft) have been supported with high pattern densities when standing supports were not operationally feasible. The most common lengths are 3 to 5 m (10 to 16 ft). An important physical characteristic is that PC-strand has an ASTM minimum elongation requirement of 4%. For comparison purposes, the ASTM 432-08 Standard Specifications for Roof and Rock Bolts and Accessories specifies elongation requirements for traditional roof bolts are a minimum of 12% for grade 40, 9% for grade 60, and 8% for grade 75 materials, respectively. Traditional roof bolts can stretch and elongate twice the length that cable bolts can, which makes design considerations challenging."

Jan 1, 2010

By Behdeen Oraee-Mirzamani

Tunnel stability has an important role in the production process of an underground coal mine. There are various methods for analysing tunnel stability, such as numerical methods and analytical methods. In this paper, numerical methods (Phase2 software) have been used to determine tunnel wall displacement in a mining tunnel of the Parvade underground coal mine. The Ground Reaction Curve has also been drawn using analytical methods to determine tunnel wall displacement. The comparison of results from the numerical method and the analytical method show a noteworthy difference in the tunnel wall displacement. The displacement calculated by the numerical method shows a lower value than that of the analytical method because the numerical method is more suited to modeling the various coal and rock layers, as well as the shape of the excavations found in coal mines. The methodology used in this paper together with the results obtained from both methods can serve as useful tools for the coal mine design engineer when determining the ground support requirements.

Jan 1, 2013

By Mark G. Colwell, Russell Frith

"An Analytical Model for Coal Mine Roof Reinforcement (AMCMRR) has been developed. AMCMRR utilizes a Factor of Safety (FOS) approach, which is commonly used in all forms of engineering. The starting point in the development of AMCMRR was an existing analytical roof behavior and roof support design methodology/model, originally developed by Colwell. This technique was used successfully in the Australian underground coal industry for roof support evaluation and design prior to and during the course of the research project, and when used, it was essentially calibrated on a site by site basis.It has long been recognized that bolts and longer tendons can modify the behavior and load bearing capacity of the reinforced roof via the concept of beam building. The break-through in developing AMCMRR was combining the original analytical model with a comprehensive database (associated with Australian collieries) to effectively quantify this reinforcing effect, and this in turn provided the ""platform"" by which this analytical model can be calibrated for the entire Australian underground coal industry.This paper focuses on the application and use of AMCMRR and the analyses undertaken to quantify the reinforcement beam building offers to the immediate roof. Furthermore, this paper demonstrates that a combined empirical and analytical approach is currently the most practical way of developing credible geotechnical design tools for the Australian or any other underground coal industry.BACKGROUNDBy the start of 2006 the ALTS (Analysis of Longwall Tailgate Serviceability-Colwell et al., 2003) and ADRS (Analysis and Design of Rib Support-Colwell, 2006) design methodologies were being routinely and widely used within the Australian underground coal industry. As a result of their success, Colwell Geotechnical Services commenced a research project entitled, ""The Future Development and Integration of ALTS & ADRS for Improved Underground Roadway Design. "" The project (which became known as the ALTS 2006 Project) was funded directly by several of the major coal producers as well as individual Australian collieries."

Jan 1, 2010

By Denise Müller, Axel Preusse

"Due to multilateral underground use, mining subsidence is discussed more and more with regard to issues other than mining, such as post-mining topics, storage, or geothermal use. These discussions and the influence of the energy policy is why the situation in Germany is described as a transition from active to abandoned mining. Many PhD theses have been written within the last 20 years—every single one with a different topic but all with the same issue—the effects and challenges of mining subsidence.These challenges start with the research regarding geological and hydrogeological conditions, which is the basis for calculations like the angle of draw or predictions of subsidence due to water table drawdown. Furthermore, the research investigates issues like risk-management and financial planning. One of these issues is post-mining calculations; others include potential hazards of storage or the use of geothermal energy.This paper outlines an overview of German mining and the consequences due to subsidence. It deals with an overview of the circumstances related to hard coal mining, lignite mining, the use of geothermal energy, gas, and opportunities regarding underground storage. Basically, it describes the essential steps of processing mining subsidence, starting with monitoring to forecast and up to safety measures.With a glance back to the applied research of the prior two decades, we compare given forecasts with experiences already gained.Even though mining decreases, ground control does not.INTRODUCTIONAfter the Second World War, an economic recovery started in Germany, during which the mining industry provided an advantage. Areas like the Ruhr District or Saarland were characterized by hard coal mining. In addition, there was lignite mining in the Rhenish mining area and the middle German coal district. In the Lausitz area, there were gravel and sand companies for the construction industry and many other medium-sized mining companies. Especially in the Ruhr District and in Saarland, where large coal fields were built, mining played a major role. The number of mines increased, and the negative effects on the terrain got bigger. While minor open pits or quarries have influences on the landscape only, large open pits and underground mining lead to significant ground movements. This results in a larger importance of mining subsidence engineering. Calculations of subsidence and forecasts have been developed and refined within the last several years. Due to the fact that the mining areas were and still are densely populated, the forecasts are getting more and more precise."

Jan 1, 2018

By David K. Ingram

The objective of this U.S. Bureau of Mines (USBM) investigation was to characterize overburden response due to longwall mining. Subsurface strata and surface deformations were monitored at two sites in southeastern Ohio. Site A included two adjacent longwall panels. Site B consisted of one longwall panel. Both sites had similar mine geometries and overburden thicknesses. The major difference between the two sites was the rock strata within the overburden. Multipoint borehole extensometers (MPBX) were employed to measure subsurface displacements. Survey monuments were installed above the centerline and profile of each panel to measure surface deformations. Subsidence of the surface was observed before and after movement was detected in the MPBX units. Initial and final displacement of the MPBX units occurred at the same time at both sites. No deformation was detected outside the panel area. The development of overburden deformation was different over each panel. The final subsurface failure characteristics also varied between panels.

Jan 1, 1994

By Dale A. Didcoct

Through the combined efforts of the C. S. Bureau of Mines, the coal industry, and Burrell Construction and Supply Company, New Kensington, PA, a steel fiber reinforced concrete crib block to improve coal mine safety in the area of roof control has been developed and is currently in use commercially. The development objective was to improve health and safety conditions with a stiffer, stronger, nonflammable roof support at a competitive cost. During the time this method of roof control has been in use in the mining industry, it has proven to be both functionally and economically effective.

Jan 1, 1982

By D. L. Price

This paper presents a method of measuring field power consumption of shearers and deriving specific energy consumption versus shearer haulage speed performance curves. A description of a computer program which simulates the cutting action of a shearer drum is presented. A comparison between the field specific energy curves and the computer simulation results is made. The simulation results compare well with the field data where all the coal seam is being cut by the shearer. The computer simulation results give hack-calculated field pick force cutting characteristics, which allow the performance of the shearer to be predicted for other operating conditions, e.g. effect of changes to pick lacing, effect of changing the drum rotational speed, allows the calculation of power requirements for a particular production rate.

Jan 1, 1992

By Joseph C. Zelanko

Cable bolt support techniques. including hardware and anchorage systems, continue to evolve to meet U.S. mining requirements. For cable support systems to be successfully implemented into new ground control areas, the mechanics of this support and the potential range of performance need to be better understood. To contribute to this understanding, a series of 36 pull tests were performed on 10 ft long cable bolts using various combinations of hole diameters, resin formulations, anchor types, and with and without resin dams. These tests provided insight as to the influence of these four parameters on cable system performance. Performance was assessed in terms of support capacity (maximum load attained in a pull test), system stiffness (assessed from two intervals of load-deformation), and from the general load-deformation response. Three characteristic load-deformation responses were observed. An Analysis of Variance identified a number of main effects and interactions of significance to support capacity and stiffness. The factorial experiment performed in this study provides insight to the effects of several design parameters associated with resin-anchored cable bolts.

Jan 1, 1995

By Gheorghe Oncioiu

The phenomena developed on the influence of thick coal seam no.3 mining, by horizontal slices and rocks caving roof control, in the Jiu Valley coal basin, are very complex. By analyzing the influence volume of underground faces and defining the stress and strain zones, around the faces, it is possible to evaluate the suitable powered support performances. Also, Jiu Valley thick coal seams involve about 50% of reserve balance in the main safety pillars of social, industrial and natural objectives, situated on the mining surface perimeters. For a correct design and drawing of main safety pillars complex research was done with the aim of establishing the subsidence parameters. Upper face rocks medium could be assimilated as a granular medium, which is in a permanent movement. For describing the rocks movement, respectively the ground surface displacement, was taken into account the stochastic mechanics principles. The theoretical solutions are in accordance within situ measurements.

Jan 1, 1999