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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 Winton Gale

"Rock and coal fractures and micro seismic vibration are common occurrences during development mining. It is very uncommon for coal and rock to be propelled into the roadway during normal mining operations. However, such occurrences do occur and appear to require significantly more energy than is available from strain energy release during coal cutting. The sources of energy, which can contribute to the propulsion of coal from the face or ribs, are typically strain energy from the surrounding ground, seismic energy from a rapid rupture of the ground in the vicinity, or rapid expansion of gas from within the burst source area.The aim of this paper is to briefly review the bursts that could be related to strain energy or seismic energy. However, the greatest emphasis is placed on the effect that gas within the coal could play in moderate to gassy mines.It has been found that the bursts related to the expansion of gas can occur in coal and stone. The volume of gas involved in coal bursts is typically lower than in gas outbursts; however, the process is generally similar.INTRODUCTIONA coal burst is defined as a rapid expulsion of coal (and potentially gas) from the boundary of the roadway. The volume of a burst can be variable, but volumes above 10-50m3 are noted and cause significant disruption to operations.Rock and coal fracturing is common about roadways, particularly under the influence of elevated stresses, either tectonic or related to mining abutment stress. Shear fracture is very common; however, it is very uncommon that the coal is propelled from the face or ribs as a result of fracture of the material. The nature of rock fracture about roadways under elevated stress is presented in Figure 1.A burst requires energy to propel the coal or rock from the rib or face of the roadway. The depth of material impacted may vary from 0.5m to greater than 3m inside the roadway boundary. The strength of the ground in this zone is variable depending on the nature of the coal seam (or surrounding material). Typically, this material has significant residual strength as confinement increases into the ribside.The energy required to propel this material is typically in addition to that which is associated with normal fracturing about the roadway."

Jan 1, 2018

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 Ihsan B. Tulu, Keith A. Heasley, Aanand Nandula

"The objective of this paper is to present the development of a software tool that will assist in an area calculation of the Analysis of Roof Bolting Systems (ARBS) support intensity while incorporating more detailed geology, stress, and intersection span input. In this area ARBS tool, a detailed CMRR distribution can be determined from the available geologic database at the mine. In addition, the overburden and multiple-seam stresses, as obtained from the boundary-element program LaModel, can be converted to a “pseudo-depth” which is then used as the depth input to the area ARBS calculation. Finally, the section-specific intersection spans can be determined from the mine design for input to the calculation. All this detailed area input information for ARBS is handled by the latest version of the Stability Mapping (StabMap) program, which now outputs an area ARBS suggested support density given the required input parameters. This final ARBS grid can be plotted, analyzed and overlaid on the mine map for optimum use in support design and for presentation to production personnel.INTRODUCTIONSince the inception of roof bolts in the 1940s, there has been a lack of a universally accepted roof bolting design method (Mark, 2002; Mark and Pappas, 2012). To address this situation, the National Institute of Occupational Safety and Hazard (NIOSH) developed roof support design guidelines, which were incorporated into a computer program called the Analysis of Roof Bolting Systems (ARBS). These guidelines were based on the effects of roof quality, stress, and mine geometry (Mark, Molinda and Dolinar, 2001). The roof rock quality in ARBS is represented by the Coal Mine Roof Rating (CMRR), the depth is used as a surrogate for the stress, and the intersection span serves to represent the mine geometry (Mark, Molinda and Dolinar, 2001). These three input parameters are used in the fundamental, empirically derived equation of ARBS to calculate a required support density factor, called ARBS, (Mark, Molinda and Dolinar, 2001):"

Jan 1, 2018

By Richard N. Campbell

The world?s ever-expanding demand for energy and coking coals has resulted in the underground mining industry looking at taking on increasingly marginal and geotechnically challenging deposits. The drivers for this change include a reduced availability of open cut reserves and a lack of remaining ?good coal leases?. The lack of plum deposits is forcing some companies wanting to enter the coal supply market to purchase and operate in higher risk, lower margin areas. As geotechnical professionals, we are expected to develop strategies to facilitate safe and productive mining in ground that once would have been avoided. To be successful in these reserves, we are required to use every tool available, from exploration data to longwall automation, and invent or reinvent some new tools along the way. This paper presents geotechnical case studies of challenges in longwall mining and some of the methods developed and used to allow longwall mining to succeed where others said we would fail.

Jan 1, 2014

By Tom Vandergritft

With advances in system design driving higher productivity, safety, and coal recovery, highwall mining is becoming an attractive option for extending reserve life at surface mines. Typically, highwall mining is performed by contract, with the system owner charging the mining company on a per ton basis, plus a mobilization fee. For this arrangement to benefit both parties, geotechnical planning is required to minimize risk to highwall mining personnel and equipment, while maximizing coal recovery. This paper discusses how highwall mining has been successfully implemented at a large surface coal mine in Colorado, including design procedures, operational factors, and productivity. The operation includes an area where four seams are mined in succession from the lowermost upward, requiring careful attention to seam interaction issues.

Jan 1, 2005

By R. Quentin Eades, Kyle Perry

"Surface mines continue to implement highwalls for several reasons, such as increasing recovery, improving margins, and justifying higher stripping ratios. Highwall stability is a complex issue that is dependent upon a variety of mining and geologic factors, and a safe design is necessary for a successful surface operation. To improve highwall stability, it is important to understand the connection between local geology and blasting.Explosives are employed throughout the mining industry for primary rock breakage. There are a number of controlled blasting techniques that can be implemented to improve highwall stability. These include line drilling, smooth wall blasting, trim blasting, buffer blasting, air decking, and presplitting. Each of these techniques have associated advantages and disadvantages. Understanding local geology is necessary for selecting the appropriate controlled blasting technique. Furthermore, understanding the limitations and conditions for successful implementation of each technique is necessary. A discussion of the impact of geologic conditions on highwall stability is provided. Additionally, discussion is provided for the successful incorporation of the controlled blasting techniques listed above, and the associated mining and geologic factors that influence the selection and design of controlled blasting plans. Finally, a new methodology is proposed.INTRODUCTIONExplosives are used throughout the mining industry as the standard for primary rock breakage, a critical part of the mining cycle. In 2015, the U.S.. consumed 2.2 million tons of explosives (Apodaca, 2015). The coal mining industry accounted for the majority of explosive consumption, accounting for approximately 63% of total explosives. The quarrying and nonmetal mining industries accounted for 12% of explosive consumption, and the metal mining industry accounted for 9% (Apodaca, 2015). This constitutes 84% of the explosives used in the U.S. However, the energy released during the detonation process is often in excess of that required to adequately fragment the surrounding rock (Jhanwar and Jethwa, 2000). This excessive energy, along with over confinement and poor blast geometry, will cause damage to the undisturbed rock mass beyond the intended boundary of the blast. This event is known as overbreak or back-break (ISEE, 2011)."

Jan 1, 2018

By Dan Payne

Roof falls and other ground control incidents make up a significant portion of fatal accidents in underground mines. BHP Billiton has undergone a review of all fatalities in their operations and divided these into 10 fundamental categories of which underground ground control is one. Each underground roof fall fatality was investigated and the root causes workshopped to develop a protocol for the control of fatalities due to falls of ground. This protocol sets out 22 requirements which each BHP Billiton underground mine site must comply with. This paper describes the development, requirements and application of the protocol within BHP Billiton.

Jan 1, 2006

By André C. Zingano

The domino effect in a violent pillar collapse occurs due to the redistribution of stress in the remaining pillars near the collapse, and this stress transfer occurs in the immediate and main roofs. The remaining pillars do not have enough load capacity to support this overstress and also fail, and the domino effect propagates further to the entire panel. The domino effect does not occur only due to low load capacity of the pillars, but also the roof rock mass quality, because the stress is transferred by the roof. In high competent roof without discontinuity (fault), like massive sandstone seam, the deformation of the roof is the cause of pillar collapse extension and propagation. Depending on how close it is approaching the collapse limit; the immediate and main roofs behave differently. When it is close to the collapse limit roof convergence and pillars compression occur. Conversely when it is far from the collapse limit divergence and pillars decompression occur. This is called the arc-effect. This paper studies this behavior of the roof (immediate and main roofs) using numerical modeling to simulate the roof deformation and stress distribution in the roof and pillars. This simulation represents the progression of pillar collapse and shows the zone of convergence and divergence of the roof, and also the effect of this behavior on pillar confinement. Two-dimensional plain strain model was applied to simulate the arc-effect. The simulation results were compared to those of the instrumentation that was installed before the collapse. Keywords: pillar collapse, room and pillar, numerical modeling

Jan 1, 2005

By Alan A. Campoli

"Pumpable crib support for longwall gates and ventilation bleeder entries is becoming more prevalent in United States coal mines (Figure 1). The pumpable crib selection and spacing design has been greatly refined by the full-scale testing conducted at the National Institute for Occupational Safety and Health (NIOSH) Mine Roof Simulator. The peak load on 24-, 27-, 30-, and 36- inch diameter J-Cribs is, on average, 300, 400, 450, and 650 kips, respectively. Standard J-Cribs have useful deformation of approximately 8 inches. The maximum useful deformation can be extended to 18–20 inches with an exterior reinforcement layer or an interior double wall, for all four J-Crib diameters. J-Crib diameter is primarily limited by a maximum 4.5:1 height-to-diameter aspect ratio. Spacing is controlled by immediate roof stability, anticipated pillar deformation, and roof bolting practice. Approximately 500,000 J-Cribs have been successfully placed in 18 different United States longwall coal mines. The selection and spacing of the J-Crib utilized to date is summarized for each mine.IntroductionLongwall productivity and safety depend on ground stability in gate and ventilation bleeder entries. Numerous support technologies have been developed and employed in United States longwall mines since the 1990s to replace traditional wooden cribbing. Many, if not all, of these technologies have been evaluated at the NIOSH Pittsburgh Research Laboratory since the mid-1990s (Mucho, et al., 1999). The NIOSH Mine Roof Simulator has a 3,000-kip vertical load and 24-inch displacement capacity, which has facilitated in-depth analysis of complex multimaterial support technologies like the pumpable crib. The extreme cost and human exposure risk associated with modern longwall mining prevent the trial and error development that would have been required absent the Mine Roof Simulator research. As a direct result of this research, pumpable cribs are becoming a major component of the standing support industry, providing the peak capacity and extended deformation characteristics necessary for successful gate and bleeder support. Recent research by Zhang, et al. (2012) and others have defined the required performance characteristics."

Jan 1, 2015

By Benjamin Mirabile

"Current and emerging practices to ventilate longwall gobs are prompting increased design and analysis of standing support requirements related to longwall mining. Specifically, additional design methodologies are being employed to evaluate standing supports in the #2 entry of a 3-entry longwall system.Numerical modeling will be used to evaluate the performance of standing support in the #2 entry between gobs of longwalls in the Herrin No. 6 seam. The performance of standing support in the #2 entry will be evaluated based on the following: (1) The effectiveness of standing support in maintaining an open airway in the #2 entry; (2) The interaction of standing support in the #2 entry with standing support in the longwall tailgate; and (3) Loading conditions of longwall pillars. Initial numerical modeling activities are focused on evaluating the roof to floor convergence in the #2 Entry and using the ground reaction curve concept for support design.Numerical modeling indicates that, like standing support in tailgates, supports in the #2 entry require some type of yield mechanism to withstand initial uncontrolled convergence. Numerical modeling also suggests that support density can be lower than that used in a tailgate support application. The numerical models used for initial investigation of support performance in the #2 entry are limited in their ability to evaluate support performance. The magnitude of uncontrollable convergence can be estimated with LaModel software. Near-seam conditions have not been investigated in this research since the LaModel software does not have the ability to evaluate inelastic rock behavior.IntroductionDuring the past three decades, many researchers have investigated standing support performance in longwall tailgate entries. Very little attention was paid to the middle entry of a threeentry longwall gateroad. As longwalls retreated, no personnel would travel the #2 entry, and the entry was considered part of the longwall gob. In response to recent mine disasters, regulatory agencies and operators have devoted more attention to these entries. Prior to the Upper Big Branch mine disaster, little or no secondary support was applied in these entries. Unlike secondary support in longwall tailgates, there is little empirical knowledge or quantified research specifically applied to secondary support in the #2 entry. This paper outlines initial steps used to develop a design methodology for secondary support in the #2 entry."

Jan 1, 2015

By Anton Sroka

The dimensioning of shaft safety zones is a substantial task of mining subsidence engineering. On the one hand, the coal reserves in shaft proximity are to be mined as complete as possible, because they can be made accessible economically. On the other hand, the maintenance of the shaft operation is to be ensured at each time, since shafts represent the most important link between underground and aboveground. Regarding these two criteria, this publication presents a model for the optimization of shaft safety zones. Beyond that, extraction methods in shaft safety zones are described, in particular with consideration of minimized mining influences on the shaft.

Jan 1, 2005

By Murali Gadde

Numerical simulation of cutter roof failure is a daunting coal mine excavation design issue. The complex progressive failure mechanisms associated with cutter failures are extremely difficult to replicate in computer models. However, this paper shows that with a proper selection of constitute behavior and implementation of cutting sequence, it is possible to realistically reproduce cutter failure using continuum models. Strain-softening material behavior and a systematic step-by-step model solving for a four-entry-and- three-crosscut model produced results that are similar to cutter patterns noticed in field. These results show that traditional modeling with geometries created in one model-step has limited applicability and may even provide misleading conclusions under some circumstances. Most importantly, the proposed modeling methodology provided some insights into the reasons for the inconsistent spatial distribution of cutters often noticed in coal mines. The modeling also revealed the usefulness of cutter mapping to determine the directions of in situ horizontal stresses.

Jan 1, 2005

The effects of corrosion upon the load bearing capacity and ultimate tensile strength of galvanised friction bolts were determined. Corrosion rates were measured by overcoring of the reinforcement elements in situ. Overcoring was achieved at several sites using a specifically designed overcoring drill rig. This rig has the capacity to drill up to 3.0m long 140- diameter core in any orientation and up to a collar height of 7.0m. The recovered core and friction bolt elements were pull tested in the rock mechanics laboratory at the WA School of Mines (WASM) in order to determine their load-displacement characteristics for various embedment lengths. The friction bolt elements were then analysed for rates of corrosion and tested for their ultimate tensile strength. Relationships were formed between these data and the environmental conditions to which the friction bolts were exposed, in order to determine the major factors affecting the corrosion process and how they affect bolt performance.

Jan 1, 2005

By Xianxin Shi

In surface electrical exploration the high resolution earth resistivity method (HRRM) is a very effective method for detecting abandoned drift mines workings. When the abandoned mines are more than 500 ft (150 m) deep, its detection capability reduces greatly and requires more effort to implement. In Yan Quan coal mine, Shanxi province, we tried to adapt this method for underground application. Two survey lines were designed with the spacing of current and potential poles 20 m and 10 m, respectively and measuring points at 2m. The measurement radius of I line and I1 line were 140 m and 60 m, respectively, and the infinitely far pole was 1200~2000 m from the survey line. (Note the I and II lines are located on the north and south ribs of main tunnel, respectively). The survey results showed that abandoned workings were located at 25-70m, Survey Line I and at 80-1 10m, Survey line 11. Based on this finding, the longwall panel gateroads and set up entry were properly located thereby providing safe mining of the No. 15 Coal seam. Key Words: Abandoned coal mine, High resolution earth resistivity, Underground electrical exploration

Jan 1, 2005

By Shugang Li

The layout and efficiency of the degasification system is heavily dependent on the distribution of and the methane migrating mechanism in the mining induced fractures in the overburden strata In this paper, physical modeling and numerical simulation are employed to study the mining-induced fracture zones and the stress distribution in these zones. The physical models show that both the fracture and compaction zones form a parabolic shape in the over- burden strata along the panel transverse direction. When this is generalized to the panel longitudinal direction, the shape of the mining induced fracture zone over the longwall gob can be represented by a 3-D elliptic paraboloid function. Through the observation of bed separation, fracture density and distribution pattern in the physical models, it is believed that the development of the parabolic fracture zone can be divided into three distinguishable phases. The expansion characteristics and sizes of the fracture zones can be estimated. The numerical stimulation studies can be used to estimate the extent of the stress release zones. The stress release zones can be also divided into a high compressive stress - fracture closure zone, stress relieved - fracture expansion zone, and intact zone. The methane desorption model is then used to analyze the methane migrating pattern in the fracture zone. The developed model has been verified by the results of a longwall gob degasification tests at a coal mine in Yangquan, China with a fair agreement. Such studies show that the model can provide a reasonable accurate tool for designing the gob-well degasification system for longwall mining operations.

Jan 1, 2005

By Anthony Lannacchione

There has been a persistent need to forecast roof falls so that miner's exposure to hazardous underground environments can be minimized. Several monitoring techniques have been developed and are used today with varying levels of acceptance in the mining industry. This paper examines the potential for monitoring microseismic emissions activity as a means of forecasting roof falls. The use of this activity to forecast roof falls has drawn only limited attention, resulting in a lack of published field performance data. This deficiency is being partially addressed by analyzing data obtained during longwall mining at Moonee Colliery in 1998. The Moonee data base contains a wealth of information concerning roof fall forecast parameters and the seismic alarm criteria used to develop these forecasts. Four seismic alarm criteria were developed and used by Moonee with varying degrees of success. Roof falls were forecasted 73% of the time with average forecast times of 54 minutes. Ninety percent of the predicted roof falls had a warning time, i.e., the time between warning and roof fall event, of greater than 1 minute. The fraction of forecasted roof falls decayed logarithmically as a function of warning time, until only 20% of events were predicted more than 100 minutes prior to roof falls. False alarms occurred in 50% of the warnings. Many of the false alarms were quickly followed by a cessation in mining which could have temporarily halted the on-going failure process. If mining had continued immediately after the false alarms, a roof fall may have occurred soon after. The microseismic activity collected .from Moonee Colliery demonstrates that techniques to forecast roof rock instabilities in underground mines are possible.

Jan 1, 2005

By Kot F. v. Unrug

In spite of the extensive research and accumulated experience from mining operations, an appropriate pillar design remains an open issue. Due to the shrinking reserve base, present mining operations move to more challenging conditions. There are usually thinner seams and geologic conditions are often unfavorable. For instance, mine roof and floor are weak or deteriorate rapidly when exposed to moisture fluctuations in mine atmosphere. It is common that pillars of current operations are more- squat than several decades ago when the bulk of pillar research have been carried out in thicker seams. The methods of pillars calculations were developed regionally (in particular countries) to suit design needs for the most important seams, from which the majority of coal production was coming (e.g. Pittsburg or Pond Creek seams in the eastern of US). Most of the pillar formulae use similar approach by assigning weights (using constants) to the influence of coal (seam) strength and pillar widthheight ratio on its final strength. That mechanistic approach has sound theoretical base and good data supporting its validity. However, what seems to be missing is a qualification system of the mine conditions, which are outside of the data base or do not comply with the theoretical model applied in pillar strength formulae. This paper attempts to address that issue in two major categories, first when only a drill core data are available, and second during the mine development observations can be made directly on a coal seam. The composition of a coal seam is also addressed, (which often changes rapidly across the reserve), and discussed its influence on pillar's structural performance. In summary a set of practical design rules is presented.

Jan 1, 2005

By R. Karl Zipf

Multiple seam mining interactions caused by full extraction mining, whether due to undermining or overmining, frequently involve tensile failure of the affected mine roof. The adverse ground control conditions may prevent mining for both safety and economic reasons. Prior researchers have identified the geometric, geologic and mining factors controlling multiple seam mining interactions. This numerical study examines the mechanics of these interactions using a modeling procedure that 1) incorporates the essential constitutive behavior of the rock such as strain- softening of the intact rock and shear and tensile failure along bedding planes and 2) captures the geologic variability of the rock especially the layering of weak and strong rocks and weak bedding planes. Specifically, the numerical study considered the effect of vertical stress, interburden thickness, and the immediate roof quality of the affected seam in both undermining and overmining situations. The models show that for overburden-to-interburden thickness (OBAB) ratios of less than 5, interactions do not occur, and that for OBAB more than 50, extreme interaction is a certainty. In between, the possibility of an interaction was found to depend on gob width-to-interburden thickness ratio, site specific geology and horizontal stress to rock strength ratio in addition to the OBIIB ratio. The models also showed that horizontal stress was profoundly altered well above or below a full extraction area and that these changes are likely to influence the success or failure of multiple seam mining. The role of horizontal stress in multiple seam mining interactions has received little attention in prior investigations. Four factors control the mechanics of multiple seam mining interactions: 1. vertical stress concentration 2. horizontal stress concentration 3. stress re-direction 4. bedding plane slip bands A combination of vertical and horizontal stress increase and high stress gradients in the vicinity of full extraction areas re-orients principal stresses into a very unfavorable direction. This seemingly small stress re-orientation has a profound adverse effect on bedded rock.

Jan 1, 2005

By R. Kaund

"Quantifying the rockburst consequence is of critical importance to reduce the hazards with preventative measures in underground mines and deep tunnels. Contours of energy components within a pillar model are plotted at different rockmass damage stages, and plastic strain work and released energy are proposed as indicators of rockmass damage consequence. One pillar model under different loading stiffness is simulated to assess indicators of pillar burst and the resulting damages. The results show the rockmass damage under soft loading stiffness has larger magnitude of plastic strain work and released energy than that which is under stiff loading stiffness, indicating the rockburst consequence can be quantified with plastic strain work and released energy in numerical models. With the quantified rockburst consequence, preventative measures can be taken to avoid severe hazards to mine safety.INTRODUCTIONWith the increasing demand of mineral resources and depletion of near-surface ores, the depths of underground mines have made the mining activities one of mankind’s most dangerous types of work (Ortlepp, 2005). The Mine Safety and Health Administration (MSHA) defines rockburst as “a sudden and violent failure of overstressed rock resulting in the instantaneous release of large amounts of accumulated energy.”The types of rockburst can be classified into three types: (1) strain burst, (2) pillar burst, and (3) fault slip (Müller, 1991). Strain burst is the most common type of unstable rock failure in underground openings, where the intensity and scale are usually smaller than pillar burst and fault slip (White and Whyatt, 1999; White, Williams and Whyatt, 2002; Ortlepp, 2005). The cause of strain burst can range from shattering of rock under high stress concentration to buckling of discontinuities parallel to underground openings. The occurrence of pillar burst also depends on the stress and discontinuity conditions in the rockmass, but pillar burst usually involves the sudden loss of strength in the core or foundation of a pillar (Whyatt and Blake, 2002; Kias and Ozbay, 2013; Khademian et al., 2016). Fault slip or slip burst can be either slip along pre-existing discontinuities or shear failure in the rockmass, when the shear stress is larger than shear strength in the fault (Rice, 1983; White and Whyatt, 1999; Sainoki and Mitri, 2014). The consequence of fault slip can vary from very small rockmass damage to consequential rockmass damage, but large seismic magnitude does not always result in large rockmass damage (White and Whyatt, 1999; Whyatt and Blake, 2002)."

Jan 1, 2018