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Subsidence of the ground surface can be regarded as ground movement that takes place due to the removal of mineral resources from within the ground, whether they be solid, liquid or gas, in other words due to mining of metals or stratiform deposits like coal or the abstraction of water, oil or natural gas. Subsidence is an inevitable consequence of mining, however the effects of subsidence depend on the type of deposit, the geological conditions, in particular the nature and structure of the overlying rocks or soils, the mining method and any mitigative action

Unfortunately, subsidence can have serious effects on surface structures, buildings, services and communications, and can damage agricultural land through the disruption of drainage and alteration of gradient. It also can be responsible for flooding; can lead to the sterilization of land or call for extensive remedial measures, or special con­structional design in site development. Therefore, a number of fundamental questions concerning the stability of the ground surface and structures in areas where subsidence has or is occurring require answers, these include:

·           Will subsidence occur and if so, what will be its magnitude?

·           When will subsidence happen and how will it develop?

·           What form will the subsidence take?

·           Is it practical and economical to prevent or re­duce the effects of subsidence?

Obviously, the answers to these questions may be difficult or impossible to obtain as they frequently depend on the assessment of a large number of factors and the nature of any answers that are obtained tend to be general rather than precise.

Old abandoned workings occur at shallow depth beneath the surface of many urban areas of the European Community and North America.  Such old workings can represent a hazard, especially during any subsequent redevelopment of land and the regeneration of inner city ‘brown-field’ sites.  The need for redevelopment in urban areas, together with the increasing scarcity of suitable land means that sites formerly regarded as unsuitable are now considered for building purposes. Many of the large industrial centres are underlain by rocks of Coal Measures age, coal and other minerals present in the Coal Measures being one of the reasons for the initial development of industry. Therefore, an added factor as far as redevelopment in such areas is concerned is the problem of past or existing mine workings. It, how­ever, must not be assumed that the frequent prob­lems associated with mining in these areas are only related to the extraction of coal for other materials have been and are extracted from the Coal Mea­sures. These include; fireclay, ganister, ironstones, clays, shales, mudstones and sandstones for building purposes etc. Such materials have been both mined and quarried.

Subsidence caused with coal mining may be broadly grouped into the following types:

·           Subsidence associated with coal mine entries (shafts, adits and inclines)

·           Subsidence associated with the partial extraction of coal (room and pillar workings)

·           Subsidence associated with total extraction of coal (longwall mining)

Mining data and records

One of the problems associated with old abandoned subsurface coal mine workings is that there may be no record of their existence.  For example, coal mining in Britain has been carried out for centuries but the first statutory obligation to keep mine records only dates from 1850 and it was not until 1872 that the production and retention of mine plans became compulsory for mines over a certain size.  Then in 1911, mine owners were required to maintain accurate plans of a specified scale and revise them every three months. Plans had to show the position of the mine workings in relation to surface features, including mine shafts and faults. However, even if old records exist, they frequently may be inaccurate.

Many parts of urban Britain are underlain by abandoned coal mine workings. The extent, age and condition of these workings beneath the built-up centres of towns and cities are, in most cases, poorly documented or else unknown. Even when former mine workings have been recorded, their precise locations can not be determined accurately in all situations. Abandonment plans rarely show information about the condition of the workings such as whether the mine openings have been stowed to reduce the risk of collapse, or the type of support systems used. In other instances mine plans may be have been produced to be completely misleading showing shafts and adits in regions where coal was not actually mined. This was practised in the 18th century, when near surface coal seams on private land were “robbed” of their reserves. Upon completion of the mining the shafts were purposely mislocated on the abandonment plans in an attempt to reduce suspicion of these ‘bogus’ mining operations.   Other similar activities included the construction of an underground dry-stone wall to disguise the area of worked coal, from a mine owner or mine inspector. On abandonment, the mine plans did not show that this area of coal had been extracted, the purpose of this was to avoid the payment of royalties. Some mine plans may show numerous geological faults that do not exist. The addition of these ‘bogus’ faults to the mine plans, in the days of private ownership, was for the non-payment of the full amount of royalties, as  the faulted coal was tax-free.

 Summary of underground coal mining methods

Adits, drifts (inclines) and early shafts

Coal has been mined in Britain from at least Roman times but mining did not begin to be carried out on a significant scale until the thirteenth century. Drifts and adits into shallow workings usually were situ­ated at the base of quarries and open pits or along the coal outcrops in areas of hills.  The workings extended as far as natural drainage and ventilation permitted.

The earliest shafts were circular or rectangular and mostly less than 2 metres across. They would have been unlined, or else had minimal temporary timber support. Later, more permanent shafts had brick, stone, or timber linings; cast iron rings (tubbing) were used when passing through water-bearing horizons. Modern shafts, lined with reinforced concrete, are circular and may have diameters exceeding 5 metres. Most collieries had two shafts, many had more.

Early shafts often received minimal treatment on abandonment. Commonly, the shaft was backfilled with soil and debris on to a timber staging or sometimes a wedged cage only a few metres below ground level. Below this, the shaft was left open, and frequently became flooded. In time the timber staging rotted and eventually failed, causing dangerous collapses. Following the Lofthouse Colliery disaster in 1973 in which seven miners died when a working coal face intersected an unsuspected water-filled old shaft, the National Coal Board initiated a programme of proving as many of these old shafts as possible, filling and capping them to render them safe. However, it should be emphasised that on the exposed coalfields there are probably numerous old shafts and shallow workings in existence which are still unrecorded. These present a potential subsidence hazard and provide pathways for groundwater recharge and/or minewater discharge, and mine gas emissions. Current practice on abandonment is for shafts to be filled with limestone chippings, brick or concrete rubble, or colliery spoil, with a concrete capping at the surface. Clay is used to seal water-bearing horizons, usually following removal of the shaft lining.

Underground roadways used for access and ventilation and not directly for coal extraction can total tens of kilometres in length at any one colliery, and be complexly interlinked, including cross-measure drifts from seam to seam. Modern practice is to use steel arch girders to support both main roadways (which may need to remain open for the life of the colliery) and also many subsidiary roadways. Older roadways were timber supported, or where there was a strong roof, left unsupported.

On abandonment, steel supports were sometimes salvaged for scrap, but in many cases the roadways were just left open, with no attempt to seal them other than ‘stoppings’ (barriers a few metres thick) at the entrances to particular mining districts, or adjacent to the shafts.

Although many roadways will eventually close completely, especially where driven through weak mudrocks, others will remain open to a degree for very many years, particularly at shallow depths, where steel supports have been left in or where there is a strong sandstone roof. Old, unrecorded, partly-open roadways have been frequently encountered during opencast operations.

Modern high-productivity retreat mining does not require continued roadway access adjacent to the goaf areas. Most recently, the practice of roof-bolting for limited-life roadway support is increasing. Consequently it is more likely in retreat mining layouts that complete roadway collapse will occur after abandonment

Bell pits

By the fourteenth century outcrop workings had largely given way to bell pits. The shafts of bell pits rarely exceeded about 12 m in depth and their diameter was usually around 1.5 m. Because bell pits were very shallow workings, they tended to be concentrated near coal outcrops where the coal was more or less horizontal or had a small amount of dip.  Indeed, the outcrop of a seam in rural areas may be delineated by a series of bell pits and associated mounds of spoil.  Obviously, bell pitting is a feature of coalfield areas where the superficial cover is thin. Extrac­tion was carried on around the shaft until such times as roof support became impossible, then another shaft was sunk nearby. Hence, where such mining went on, the number of bell pits may be very numerous. If bell pits were backfilled, then the state of compaction of the fill generally is unsatisfactory.  It generally is impossible to predict the distribution or amount of void space in the ground associated with the old bell pits.  This can present problems in terms of development or redevelopment of a site.

Earliest workings, generally up to the 17th century, exploited seams exposed at or near the surface. This was either by adits, i.e. driving roadways directly into the coal and following it down-dip, or by bell pits which involved sinking a shallow shaft through the overlying measures to reach the seam. Such workings were limited to seams at or close to outcrop, seldom reaching depths of more than 10 metres, and as this was prior to mechanised pumping, above the water table. These old workings are now mostly infilled with collapsed material (often exposed in modern opencast mines) but the permanently disturbed ground may well allow increased infiltration of surface and meteoric water, resulting in enhanced recharge. This is particularly important when somewhat more advanced workings extending considerable distances down-dip are in contact with these shallow workings.

Room & pillar

Room and pillar (also known as ‘pillar and stall’ or ‘bord and pillar’) methods replaced bell pits in the 16th and 17th centuries. Access to the coal was by adits, drifts (inclined cross-measure roadways) or vertical shafts. The coal was extracted by a grid-like series of in-seam roadways with pillars of coal left to support the roof, extra timber props being set where necessary. Coal pillars were frequently extracted or ‘robbed’ immediately prior to abandoning a particular section or ‘district’ of the mine although main access roadways were maintained by leaving the adjacent coal pillars intact.

When a coal seam occurred at more than about 7 m below the surface, bell pit mining tended to be replaced by headings that radiated into the coal seam for short distances around the shaft. The pil­lars of coal between the headings generally repre­sented the only type of support to the overlying strata. The layout of a mine was unplanned and simply consisted of a complex of interconnected headings. Hence, the support pillars were irregular in shape and size.

Because of the scarcity of timber, the de­mand for coal increased in the sixteenth century and led to the development of the pillar and stall method of ex­traction. Underground workings were shallow and not extensive, for example, they rarely penetrated more than 40 m from the shaft. Indeed, when such limits were reached, it was usually less costly to abandon a pit and sink another shaft nearby. Work­ings extending 200 m from the shaft were excep­tional even at the end of the seventeenth century, the shaft itself usually being less than 60 m deep.

In very early mining the remnant pillars and voids (variously referred to as stalls, rooms, or bords) usually differed in size and arrangement, but with time mining became more systematic and pillars of more or less uniform shape were formed by driving intersecting roadways in the seam. Also, there was a general tendency for the size of stalls to increase. In the nine­teenth century the normal width of stalls varied from 1.83 to 4.57 m, the extraction ratio vary­ing from 30 to 70%. However, in the USA pillar arrangement became more sys­tematic during the second half of the nineteenth century. The stalls were 1.5 to 1.8 m wide and al­ternated with pillars of equal width so that the ex­traction ratio did not exceed 50%. In the 1890s the width of the stalls increased to between 6 and 7.3 m and pillar dimensions to between 3 and 5.4 m.

Longwall mining

At the beginning of the 20th century early longwall mining became established with the introduction of coal cutting machines. Under-cut coal was shot-fired down and loaded by hand on to conveyor belts. This took place along a continuous length of up to several hundred metres of exposed coal (the ‘longwall face’). Roof support was by timber props, later steel and hydraulic props. Access roadways allowed ventilation and coal transport. The face progressed by extracting successive ‘strips’ of coal; the supports and conveyors were manually advanced to their new positions. Main roadways to the face were protected by means of ‘packs’ consisting of dry-stone wall cells constructed of waste rock, infilled with debris, built up to support the roof (National Coal Board 1957). In order to control the stresses on the coal face, packs were often built at intervals in the goaf areas, being extended continually as the coal face advanced Elsewhere, roof rocks were allowed to collapse into the goaf.

Modern longwall mining developed in the latter half of this century, and has become fully mechanised. Rectangular ‘panels’ of coal generally 200 - 250 metres wide, and perhaps several thousand metres long in favourable geological conditions, are extracted using a coal cutting machine mounted on a steel conveyor. The machine travels along the length of the face cutting a strip of coal which falls on to the conveyor. The face is supported by a closely spaced series of hydraulically powered supports which advance up to the newly exposed coal as the cutting machine has passed. The unsupported roof is allowed to cave behind and forms the goaf. At each end, the coal face connects with an arch- or rectangular- section roadway with steel supports for coal transport, ventilation and supplies access. Advancing longwall panels require the access roadways to be maintained and are frequently protected by roadside packs.

With the coming of the Industrial Revolution the demand for coal in Britain increased.  Longwall mining evolved more or less at the same time, probably originating first in the Shropshire Coalfield. However, longwall mining has been used to mine other stratiform deposits, although it primarily is used to mine coal. The great majority of the coal mined in Britain in the twentieth century and at present, although now greatly reduced in amount, is by panel working, which is a develop­ment of the longwall system suited to mechanized extraction techniques. This method of mining involves the total extraction of a series of panels of coal that are separated by pillars whose width is small compared to overburden thickness. The coal is exposed at a face 30 to 300 m in width between two parallel roadways. The roof is supported temporarily at the working face, and in and near the roadways.  After the coal has been won and loaded the face supports are advanced leaving the rock, in the areas where coal has been removed, to collapse. This leads to the subsidence of the ground surface.

Subsidence associated with mine entries (shafts & adits)

The most significant hazard which an abandoned mineshaft can present is sudden, unexpected collapse.  However, this is rare, since crown hole development (the appearance of a hole at the ground surface) is usually preceded by warning signs of subtle deformation of the ground surface and trough subsidence above the shaft. This may not be the case in a region where the ground surface above mineshaft consists of concrete or tarmacadam. When a shaft does undergo sudden catastrophic failure, the results can be dramatic. This is particularly true if shaft collapse occurs in a densely populated urban environment. The potential hazards presented by abandoned shafts include:

·         Collapse or movement of the ground. This may occur suddenly, or gradually.

·         The discharge of acid or ochrous minewaters which can result in pollution of water courses and aquifers.

·         Flooding of basements, building and structural foundations.

·         Emission of mine gases.

·         Accidental entry: injury or death is almost inevitable following a fall down a shaft. Flooded shafts compound the risk with the added danger of drowning, suffocation or poisoning by gas; collapse of the shaft is also possible, once disturbed.

Subsidence associated room and pillar workings (partial extraction)

Pillar deterioration and failure

The deterioration of pillars, over time, may lead to subsidence. The mechanisms of failure will depend on several factors such as the depth of extraction, width and depth ratio of the workings. Individual pillars in dipping seams tend to be less stable than those in horizontal seams since the overburden produces a shear force on the pillar. In addition, the great­est stress occurs at the edges of pillars, between pillar and roof or between pillar and floor. If a pillar is highly jointed, then its margin may fail and fall away (known as spalling) under relatively low stress.

Yielding of a large number of pillars can bring about a shallow broad subsidence over a large surface area that is referred to as a 'sag'. The ground surface in a sag displaces radially inwards towards the area of maximum subsidence.  This inward radial movement generates tangential compressive strain and circumferential tension fractures frequently are developed.  Sag movements depend on the mine layout, in particular the extraction ratio, and geology, as well as the topographic conditions at the surface. They tend to develop rather suddenly, the major initial movements lasting, in some instances, for about a week, with subsequent displacements occurring over varying periods of time.  The initial movements can produce a relatively steep-sided bowl-shaped area. Nonetheless, the shape of a sag profile can vary appreciably and because it varies with mine layout and geological conditions, it can be difficult to predict accurately.  Normally, the greater the maximum subsidence, the greater is the likelihood of variation in the profile.  Maximum profile slopes and curvatures frequently increase with increasing subsidence.  The magnitude of surface tensile and compressive strains can range from slight to severe. 

Slow deterioration and failure of pillars may take place years after mining operations have ceased, although observations at shallow depth in coal mines and the re­sistance of coal to weathering in pillared workings suggests that this is a relatively uncommon feature at depths of less than 30 m. However, old workings affect the pattern of groundwater drainage, which in turn may influence pillar deterioration.  On the other hand, small pillars in coal mines of earlier workings may be crushed out once the overburden exceeds 50 or 60 m.

Very frequently, when a mine neared the end of its life, the pillars were robbed. Extraction of pillars during the retreat phase simulates the longwall surface con­dition although it can never be assumed that all pillars have been removed. At mod­erate depths pillars, particularly pillar remnants are probably crushed and the goaf (the worked out area) compacted, but at shallow depths lower crush­ing pressures may mean the closure is variable. This is likely to cause foundation problems when large or sensitive structures are to be erected above. 

Floor heave

In coal mines the floor of an extraction area frequently heaves this being especially characteristic of areas where argillaceous rocks, notably fireclays, form the floor. Floor heave can occur at shallow depth, for example, old roadways at less than 20 m depth have at times been completely closed. Obviously, significant floor heave places a constraint on pillars and reduces the void volume thus pillar spalling and void migration are reduced.

Squeezes or crushes sometimes occur in a coal mine as a result of the pillars being punched into either the roof or floor beds. In such cases the roof or floor may have been weakened or altered by the action of groundwater or weathering. Once again any resulting surface subsidence adopts a trough-like or basin form, and minor strain and tilt problems occur around the periphery of the basin thereby pro­duced.

Although much subsidence often is slow it may be quickened by the ingress of water into the workings. In particular, softening of argillaceous material once coal has been removed can give rise to bearing capacity failure of pillars.  Softening is brought about by slaking or swelling on the one hand or creep or strain softening due to sustained loading on the other.  The time taken for such pillar failure and associated subsidence to occur varies.

Even if pillars are relatively stable the strata above a worked out area (i.e. a room or stall) may be affected by void migration. This can take place within a few months of or a very long period of years after mining and in Britain is a much more serious problem than pillar collapse.

Void migration

Void mi­gration develops when roof rock falls into the worked out areas. When this takes place the material involved in the fall bulks, which means that migration is eventually arrested, alternatively upward migration may be halted by a strong competent bed of rock that acts as a beam spanning the void. Nevertheless, the process can, at shallow depth, continue upwards to the ground surface leading to the sudden appearance of a crown hole. The geometry of crown holes is influenced by the nature and thickness of the overlying strata, the state of stress existing in the roof rocks and the height of the extraction but generally the surface shape of crown holes is circular or elliptical. 

The factors that influence whether or not void migration will take place include; the width of the unsupported span, the height of the workings, the nature of the cover rocks particularly their shear strength and the incidence and geometry of discon­tinuities, the thickness and dip of the seam, the depth of overburden and the groundwater regime.

Four methods that have been used to predict the collapse of roof strata above stalls.  These are (a) clamped beam analysis that considers the tensile strength of the immediate roof rocks (b) bulking equations that consider the maximum height of collapse before a void is choked (c) arching theories that estimate the height to which a collapse will occur before a stable arch and (d) coefficients based on experience and field observations that act as multipliers of either seam thickness or span width. Voids can adopt various geometrical forms such conical, wedge and rectangular collapses and therefore dif­ferent expressions must be used to calculate void migration. It frequently is maintained that:

·         For a particular width of mine opening the height of collapse or mi­gration is a function of the original height of the mine opening and the bulking factor of the overlying strata.

·         Void migration is directly proportional to the thickness of seam mined, assuming that the total thickness is worked, and inversely proportional to the change in volume of the collapsed material.

·         The height of collapse in pillared workings in coal is frequently proportional to the width of the excavation and that the larger the span, the more likely is collapse to occur. 

·         The maximum height of migration in exceptional cases might extend to 10 times the height of the original stall; however, it generally is 3 to 5 times the stall height.

·         Depth of cover should not include superficial deposits or made-ground since low bulking factors are characteristic of these materials. 

·         Weak superficial deposits may flow into voids that have reached rockhead, thereby forming features that may vary from a gentle dishing of the surface to inverted cone-like depressions of large diameter.

·         In a sequence of differing rock types, if a competent rock beam is to span an opening, then its thickness should be equal to twice the span width in order to allow for arching to develop. 

·         A thick bed of sandstone usually will arrest a void, especially if it is located some distance above the immediate roof of the working.

·         Sandstones apart, however, most voids are bridged when the span decreases through corbelling to an acceptable width, rather than when a more competent bed is encountered.  Chimney-type collapses can occur to abnormally high levels of migration in massive strata in which the joints diverge downwards. 

·         Exceptionally, void migrations in excess of 20 times the worked height of a coal seam have been recorded.  The self-choking process may not be fulfilled in dipping seams, especially if they are affected by copious quantities of groundwater that can redistribute the fallen material.

·         The redistribution of collapsed material can lead to the formation of supervoids.  In addition, the migration of a void from a coal seam into a worked seam directly above can lead to pillar collapse in that seam with the formation of voids that are larger than the original stalls. Migration of super voids up to rockhead, then produces large scale subsidence at ground level.  Under such circumstances simple analysis according to bulking factors proves inadequate.

Total extraction and subsidence (longwall mining)

Subsidence at the surface more or less fol­lows the advance of the working face and may be regarded as immediate. Subsidence associated with longwall mining dif­fers in two important respects from that associated with abandoned pillar and stall workings, as follows:

·           Longwall mining can be predicted with a rea­sonable degree of accuracy

·           Longwall mining is more or less contem­poraneous with extraction.

Subsidence trough

Subsidence associated with longwall mining can be dealt with by surface de­velopers either by designing structures to accom­modate the surface movements or by delaying de­velopment until subsidence has ceased. However, some of the factors that influence subsidence due to longwall mining, such as the reactivation of faults, cannot be quantified with any precision.

The subsidence that occurs over a com­pletely mined out area in a flat seam is trough-shaped and extends outwards beyond the limits of mining in all directions.  In trough subsidence the resulting stratal and surface ground movements are regarded as largely contemporaneous with mining, producing more or less direct effects at the surface develop­ment. Trough shaped subsidence profiles develop tilt between adjacent points that have subsided different amounts and curvature re­sults from adjacent sections that are tilted by dif­fering amounts. 

Tilt

Maximum ground tilts are developed above the limits of the area of extraction and may be cumu­lative if more than one seam is worked up to a common boundary.  Where movements occur, points at the surface subside downwards and are displaced horizontally inwards towards the axis of the exca­vation.

Tilt of a subsidence profile is found by dividing the difference in subsidence by the distance between two points or surveying stations. The maximum tilt in each subsidence profile occurs at the point of inflection and decreases towards the centre and edges of the profile where the slope is reduced to zero. The maximum possible tilt occurs at 2.75 Smax/d or 33.35 S/d, where Smax is maximum subsidence, S is sub­sidence and d is depth of seam.  Slope profiles vary with width-depth ratios of excava­tions.  For example, the greatest maximum slope oc­curs when the width-depth ratio of an excavation is 0.45.

Curvature

Curvature can be expressed by the difference in slope between two stations or radius of curva­ture.

Strain

Strain is proportional to the ratio between the differential slope and the distance between ob­servation points. 

Differential horizontal displacements

Differential horizontal displace­ments result in a zone of apparent extension on the convex part of the subsidence profile (over the edges of the excavation) whilst a zone of compression develops on the concave section over the excavation itself.  Differential subsidence can cause substantial damage, the tensile strains thereby generated usually being the most effective in this respect. Compara­tively slight deviations in the subsidence profile are accompanied by appreciable variations in strain.  In fact, ground movement is three dimensional and movements of the vertical and two horizontal com­ponents may occur simultaneously.

Horizontal displacement along a subsidence trough is proportional to the slope of the subsidence profile. Tensile strain (e+) and compressive strain (e-) occur on both sides of the subsidence profile. The point of transition from compression to tension is referred to as the point of inflection and coincides with the point of half-maximum subsidence. Theoretically, the area under compressive strain is equal to that under tensile strain.  In a strain profile, max­imum tensile strain is located directly above or near but outside, the ribside (i.e. position of the gate roads).  Maximum compressive strain is lo­cated either above the centre of the goaf or near there. The maximum compressive strain possible occurs in sub critical openings whereas maximum possible tensile strain is found in supercritical openings.  This means that in terms of a structure that is located above the centreline of an advancing longwall panel that it is subjected initially to tensile ground strains and later to compressive strains in a direction parallel to the centreline of the panel.  At the same time, the structure is subjected to compressive strains of changing magnitude in a direction normal to the centreline of the panel.  On the other hand, a structure that is located between the centreline of a panel and the panel boundary is subjected to tensile strains of varying magnitude that fan out from the centre of the panel, as well as to compressive strains of varying magnitude that are orientated perpendicular to the tensile strains. Strain, curvature, tilt and vertical and horizontal displacements also change in magnitude and direction as a subsidence profile progresses.

Bed separation

The removal of roof support in longwall mining is followed by collapse of those rocks (strata) that are immediately above the coal seam since they are subjected to bending and tensile stresses. These broken rocks offer partial support to the superincumbent roof layers. Nevertheless, stresses in the rock mass remaining in place are significantly in­creased, and the resultant fracture and associated dilation mean that the rock strength is reduced from a peak to a residual value with loss in load bearing capacity and the redistribution of stress.  In addition, laminated rock masses may suffer bed separation. The fracture zone defined by the extent of dilation extends at least half the face width above seam level.

Angle-of-draw (limit-angle)

The surface area affected by ground movement is greater than the area worked in the seam.  The boundary of the surface area affected is defined by the limit angle or angle-of-draw, which varies from 8° to 45°, depending on the coalfield. The angle of draw may be influenced by depth, seam thickness and local geology, especially the location of self-supporting strata above the worked coal seam. For inclined seams, the surface subsidence trough is displaced towards the down-dip side. The angle-of-draw depends on the dip of the seam, it being least at the rise side of the goaf and increases towards the dip side.

Maximum subsidence

All other things being equal, the thicker the coal seam (assuming the full thickness is extracted), the larger is the surface subsidence. If more than one seam is worked simultaneously beneath the same area, then the subsidence effects are cu­mulative. The maximum possible subsidence (Smax) is: Smax = Ha, where H is seam thickness (or thickness of seam extracted) and is a subsidence factor that ranges from 0.1 to 0.9.

The subsidence factor

The subsidence factor generally is regarded as being in­dependent of depth. However, it does depend on whether or not the mined out area has been filled or packed. Unfortunately, the character of any infill and the manner by which it is placed is so variable that only qualitative assessments of the subsidence factor can be made.  In fact, it has been suggested that it is only in a single mining area where character and placement of infill are similar, that quantitative assessment of the effects of the sub­sidence factor can be made properly.

Bulking

Usually, there is an appreciable difference between the volume of mineral extracted and the amount of subsidence at the surface.  For example where maximum subsi­dence of 90% of seam thickness occurred, the volume of the subsided ground was only 70% of the coal extracted. This is mainly attributable to bulking.

In a level seam the greatest amount of subsidence occurs over the centre of the working, diminishing to zero at approximately 0.7 of the depth outside the boundaries of the panel.  However, as far as no­ticeable movement and damage are concerned a dis­tance of 0.5 times the depth is more appropriate.

Width to depth ratio

One of the most important factors influencing the amount of subsidence is the width-depth relationship of the panel removed.  The maximum subsidence in British coalfields generally began at a width-depth ratio of 1.4:1. This is the critical condition above and below which max­imum subsidence is and is not achieved respectively.

Area-of-influence

For a given point (P) on the surface, the area-of-influence in a level seam is the circle at the base of an imaginary cone with its axis passing upwards through the overlying strata to (P) at its apex. The diameter of the area equals 1.4 x seam depth.  Any workings outside this area do not affect point (P) whereas all workings within the area do.  However, all the coal from within this critical area must be extracted before point (P) undergoes maximum sub­sidence.  If only part of the critical area is worked, then point (P) only suffers partial subsidence.  Hence, the development of subsidence attributable to a giv­en working is influenced by its width in relation to its depth. Three stages were distinguished, namely, sub critical (width less than 1.4 x depth), critical (width equal to 1.4 x depth) and supercrit­ical (width greater than 1.4 x depth).

The large width-depth ratio nec­essary to cause 90% maximum subsidence usually can only be achieved in shallow workings because with deeper workings the critical area of extraction is made up of a number of panels often with narrow pillars of coal left in situ to protect one or other of the roadways. These pillars reduce the subsidence and some coalfields in Britain, as a result, had no experience of subsidence in excess of 75 to 80%. With shallow workings the supported or partially supported zones in a goaf, such as roadways and gate-side packs, compose a much greater proportion of the width than in deeper workings. Therefore, deep panels can cause more subsidence than shallow ones with the same width-depth ratio.

As long as mining is carried out within the area-of-influence of a surface point, that point continues to subside.  However, once coal has been removed from the whole area all the subsidence at the surface point will have taken place. 

Shallow workings

Ground movements over shallow workings may differ from deep work­ings, mainly because of the masking effect of thick overburdens.  For instance, for a given maximum subsidence, the curvature of the ground surface is more marked over shallow workings than over deep workings owing to the smaller distance over which the subsidence curve is spread. The horizontal strains are proportional to subsidence and inversely pro­portional to the depth of workings. The maximum slope in the ground in a subsidence trough also is proportional to the subsidence at the bottom of the trough and inversely proportional to the depth of the workings.  It follows that maximum slope is pro­portional to the maximum horizontal strain.

Time dependant subsidence

The time taken for subsidence at a surface point to be completed is more or less inversely proportional to the rate of forward advance of the workings.  The transition of movement to the surface is almost in­stantaneous, commencing when the strata at seam horizon begin to relax. Although the precise begin­ning and end of subsidence are difficult to deter­mine, measurable subsidence occurs when the face is within a distance of 0.75d (d = depth to coal seam) and reaches approximately 15% of maximum when the face is directly below a given point (P), on the surface. For all practical purposes, it is complete when the face has advanced 0.8d beyond this given point (P). Residual subsidence then occurs, those points that are subsiding fastest ex­periencing the most residual subsidence. The time factor is minimal under normal conditions.

Residual subsidence

Residual subsidence takes place at the same time as instantaneous subsidence and may continue after the latter for periods normally up to two years, where this takes place in British Coal Measures. The magnitude of residual subsidence is proportional to the rate of subsidence of the surface and is related to the mechanical properties of the rocks above the coal seam concerned.  For instance, strong rocks produce more re­sidual subsidence than weaker ones.  Residual sub­sidence rarely exceeds 10% of total subsidence if the face is stopped within the critical width, but falls to 2 to 3% if the face has passed the critical width. Very occasionally values greater than 10% have been recorded. A study of five coal mines in Britain found that residual subsidence ranged from 8 to 45% of total subsidence and continued for up to 11 years after mining operations ceased.  Residual subsidence in the Kamptee coal field, India, varied between 7.4 and 22.4% of total subsidence and took place in less than two years.  According to some researchers the maximum residual subsidence in a level seam occurs at the half-subsidence point along a longitudinal line to the workings while along a transverse line it occurs at the centre of the workings. The maximum residual subsidence in an inclined seam occurs at the ribside point.  Residual subsidence also may be influenced by, for example; mine water rebound, the collapse of old pillars, settlement of goaf and the reactivation of faults.

Dip of seam

The dip of a coal seam influences the direction in which longwall mining takes place in that when the dip exceeds 30° working commonly takes place along the strike.  The principal method of working such seams is by horizon mining, which involves driving several roadways through the strata in which the coal seams occur.  Subsidence attributable to horizon mining layouts tends to be concentrated with most subsidence troughs having their major axes parallel to the strike of the seam.  It is possible to phase longwall extractions so that the development of ground strain at the surface is more widespread (sometimes this is called harmonious mining). As pointed out above, caving of the roof behind the longwall in dipping seams tends to displace the maximum subsidence from over the centre line of the face towards the dip side, giving rise to an asymmetrical development of ground movement. Maximum subsidence occurs at the point normal to the centre of the goaf and the angle of draw depends on the dip of the seam, it being least at the rise side and increases towards the dip side.  Hence, the area-of-influence at the dip side is broader, which means that the area of tensile strain is wider.  The dip side experiences appreciably more lateral displacement for equal vertical subsidence on each side of the longwall panel and hence correspondingly increased tensile strain.  If the seam is at shallow depth, then the subsidence at the rise side of the face has a more marked effect at the surface than at the dip side, especially with the ground strain being concentrated.  Steeply dipping coal seams (e.g. over 75°) can generate large strains on the sides of a longwall working that, in turn, can lead to discontinuities being opened at the surface, along with the development of stepping. 

When very steep coal seams are mined flexuring and breakage of strata may take place normal to bedding whilst slippage and shearing take place parallel to the bedding.  This can complicate subsidence, giving rise to multiple subsidence profiles.

Mining subsidence induced landslides

Ground movement is asymmetrical about the centre of an extraction panel in areas of high relief or on slopes.  Frequently, tensile strains produced by subsidence associated with longwall mining, especially of dipping seams, can give rise to significant fissuring on steep hillsides that can be responsible for stability problems.

The high frequency occurrence of landslides, or of a single major destructive landslide, on slopes in active and abandoned mining areas, raises concerns as to whether mining has been and is a significant contributory factor in landslide generation in such areas.  However, mining induced landslides may be difficult to prove since the occurrence of landslides tends to be influenced by several other interrelated factors.  Indeed, the number of factors that influence slope stability may be numerous and varied, and interact in complex and often subtle ways.  Frequently, the final factor is simply a trigger mechanism that sets in motion a mass that already was near the point of failure.  Basically, landslides occur because the combination of forces creating movement exceed those resisting movement. Mining can be one of those forces and has the potential for triggering landslides where unfavourable ground conditions exist.  Nonetheless, an analysis of mining subsidence in relation to slopes is complex and involves both mining and geological factors.  The mining factors include the method of working, the width and depth of the extraction, and the height of the mineral worked.  Geological factors include the nature of rock types involved, the geological structure, presence of faults and the surface topography. Classic mining subsidence induced landslides have been documented in the South Wales Coalfield where these are influenced by the coal mining subsidence reactivation of reactivation of faults. An Other example occurred in Derbyshire, at Bolsover, where the failure of an escarpment underlain by Permian Magnesian Limestone, resting above productive Coal Measures, resulting in the severe damage to several houses and associated infrastructure in the early 1990s.

One of the most notable examples of landslides occurred on 29 April 1903, at the small town of Frank, in southern Alberta, Canada, when Turtle Mountain collapsed.  This resulted in one of the greatest landslides recorded in North America. At least 70 people were killed when approximately 90 million tonnes of limestone fell some 750 m from the peak of the mountain and rose 145 m up the slope on the opposite side of the valley. 

Opencast excavations advancing towards and parallel to rib side positions of underground workings are particularly prone to failure, especially if advancing up dip. The St. Aiden’s extension opencast coal site is located approximately 10 km south east of Leeds, on the flood plain of the River Aire, in Yorkshire, England. The bedrock succession consists of Upper Carboniferous (Westphalian) Coal Measures. Several seams had been worked in the area by underground mining and at the site by opencast mining. A massive failure occurred in the wall of the opencast workings in March 1985, causing the displacement approximately 600 000 m³ of Coal Measures strata into the void, the failure measuring about 350 m long, 120 m wide and 50 m high. This caused a breach in the riverbanks and flood control levees along the River Aire for at least three days, which resulted in flooding the opencast void. Around 17 million m³ of water flowed into the opencast workings forming a lake up to 70 m deep and covering an area of about 100 ha. Coal mining operations were suspended for ten years, sterilizing approximately 2 million tonnes of coal reserves. Remediation involved the re-routing of the river and a canal. The pumping of the flood waters from the workings and the re-establishment of new mining operations were estimated to have cost approximately £36 million

Geology and subsidence due to longwall mining

In ad­dition to the rate of advance and size of critical area, the duration of surface subsidence depends on geo­logical conditions, especially the near surface rocks and superficial deposits, depth of extraction, type of packing and previous extraction. For example, it lasts longer for thick bedded or stronger overburden and for complete caving. Depth, in particular, influences the rate of subsidence.  Firstly, this is because the diameter of the area-of-influence and therefore the time taken for a working, with a given rate of ad­vance, to transverse it, increases with depth and, secondly, because at greater depths several workings may be necessary before the area-of -nfluence is completely worked out.  Consequently, the time that elapses before subsidence is complete varies ac­cording to circumstances.

Basic ground move­ments are fairly consistent in typical Coal Measures rocks.  Such movements decrease with increasing depth and generally can be predicted at the surface to within ±10% in exposed coalfields. The situation can be complicated if seams have been worked previously, especially by partial extraction methods. Interaction effects tend to enhance the ba­sic movements and may give rise to erratic subsi­dence. If a seam has been worked previously by total extraction methods, this frequently causes the ef­fective movements to increase by about 10% when another seam is worked subsequently above or below. This is because the first seam extracted will have disturbed the ground.

Engineering properties of surface soils and rocks

Many sand, silt and clay soils may deform uniformly in a subsiding area, but there are some examples of non-uniform soil behaviour.  These included soils on slopes that might shear along one or more surfaces (e.g. a soil-rock interface), resulting in soil creep hump or slippage thereby distorting the distribution of ground strain.  Soils may be loosened or consolidate as a consequence of ground movements. The latter is likely to occur if the water table is lowered by fractures developing due to subsidence, which bring about drainage of near surface sediments.  In addition, soil may washed into such fractures.  The influence of soil on ground strain depended on its thickness, as well as its properties.

Superficial deposits are often sufficiently flexible to ob­scure the effects of movements at rockhead. In par­ticular, thick deposits of glacial till tend to obscure tensile effects. On the other hand, superficial deposits may allow movements to affect larger areas than otherwise.

Rigid inclusions in stratal sequences above coal seams being mined, such as sandstone lenses in mudrocks, often present problems when subjected to compressive ground strains. These lenses tend to be forced upwards by the compressive forces with ob­vious consequences to foundations placed on or over them. This process may also result in the generation of compressional humps on the ground surface.

The subsidence factor decreases with increasing proportion of strong rocks in the overburden above a coal seam.  Stronger rocks, such as strong sandstones, may behave as cantilever beams take longer to react to ground movements induced by longwall mining.  As a consequence, ground movements at the surface take place more slowly and take more time to develop maximum values.   Non-uniform subsidence therefore may occur above a panel when abnormally thick beds of sandstone are present in the overburden or when facies changes give rise to irregular displacements in other rock units.  In addition, bed separation can occur between competent and weak strata, and that such separation is more permanent over the ribside of a panel.

The necessary readjustment in weak strata to sub­sidence effects usually can be accommodated by small movements along joints. However, as the strength of the surface rock and the joint spacing increases so the movement tends to become con­centrated at fewer points so that in massive limestones and sandstones movements may be restricted to master joints. Hence, well developed joints or fissures in such rocks concentrate differential displacement. Tensile and compressive strains many times the ba­sic value has been observed at such discontinuities. It is quite common for the total lateral movement caused by a given working to concentrate in such a manner. In such instances, no strain is measurable on either side of the discontinuity concerned.

Although some authorities have been of the opinion that fissures are formed in surface strata by longwall mining and that their orientation is aligned in relation to the geometry of the workings (one set of fissures running parallel to the coal face and the other parallel to the ribside), this is most unlikely except perhaps in the case of near surface workings.  For instance, the ground strains at the surface generated by extraction of a seam at 500 m depth are small and could not give rise to major fissures in massive rock.  On the other hand, they could open existing joints.  Hence, the relationship between mine geometry and surface fissuring is probably coincidental.  Some fissures may be associated with the reactivation or dilation of faults.

In concealed coalfields the strata overlying the coal bearing measures often influence the basic movements developed by subsidence.  In fact, abnormal subsi­dence behaviour and inconsistent movements are much more common in concealed than exposed coalfields. The occurrence of abnormally thick beds of sandstone can modify stratal movement due to mining, especially when width-depth ratios are small. Such beds may resist deflection, in which case stratal separation occurs and the effective move­ments at the surface are appreciably less than otherwise would be expected. The differences in behaviour disappear when the extraction becomes wide enough for the sandstone to collapse, then subsidence be­haviour reverts to normal. A predominant jointing pattern in the Permo-Triassic strata overlying the Coal Measures in Nottinghamshire, England.  In both the Sherwood Sandstone (Triassic) and the Magnesian Limestone (Permian) there was a tendency to produce less subsidence than that predicted for width-depth ratios exceeding 1.0.  This was due to the two formations behaving as block jointed media in which the individual blocks did not return exactly to their former positions after compressional ground movement had ceased. Obviously, the friction between the blocks plays an important role.  On the other hand, rock type did not appear to have a marked influence when the width-depth ratio was less than 1.0. 

Where the surface rocks consisted of Sherwood Sandstone, then surface strain was noticeably more irregular and tensile strain was higher than when Magnesian Limestone occurred at the surface. By contrast, there was no recognizable difference in the maximum compressional strains recorded.  The type of rock did not appear to have a notable influence on the maximum ground slope resulting from subsidence.  The relationship between subsidence over the ribside and width-depth ratio in the Sherwood Sandstone again suggested that block behaviour occurred at the surface.  Furthermore, the maximum tensile strain appeared to be displaced further away from the extraction area, that is, towards the area of less constraint on the line of surface blocks.  Hence, there is a greater likelihood of discontinuities opening further from the compressional zone rather than nearer to it.  This did not appear valid for width-depth ratios less than 0.4, which suggests that magnitudes of strain need to be sufficiently large to promote surface block behaviour.  However, in this situation it appears that the discontinuities in the Magnesian Limestone do not necessarily influence subsidence behaviour as much as those in the Sherwood Sandstone and that the limestone tends to behave normally. Such block movement is controlled primarily by the nature of the discontinuities in the sandstone.

There are many areas where joints in rockhead strata, beneath overlying superficial deposits, have been opened and the gape been enlarged by mining subsidence.  Where the superficial deposits are granular and permeable, there is a tendency for sub-surface water to wash them into these discontinuities, causing localized surface subsidence. The exact locations of joints that may open cannot be predicted but can adversely affect residential, commercial or industrial developments. The jointing pattern, however, can be exposed on site by digging trenches through the overburden.  When joints are found, their condition (e.g. open or choked) is recorded.  In this way the position, orientation, elevation and width of all joints encountered in trenches can be recorded on a site plan. In some cases fissures may be masked by the presence of soil bridges, although these may collapse several years after mining has ceased or during periods of prolonged heavy rain.

Deformation of the ground is brought about by several different mechanisms depending, in part, on the nature of the strata concerned.  For instance, a fireclay beneath a coal seam will flow into roadways, whilst a sandstone roof typically breaks at a forward angle over the face. In Britain gross fracturing in the roof rocks is not believed to extend upwards much more than three times the seam thickness, although minor fractures and bed separation may continue some distance fur­ther. As a consequence, most of the ground that undergoes deformation as a result of longwall extraction has been regarded as a continuous medium. 

Compacted fill

A thick compacted fill immediately overlying a jointed rock mass, provided it is well graded and possesses some cohesion, can form an arch between the adjacent surfaces of a joint that is opened by subsidence.  On the other hand, reliance on a certain thickness of soil cover to provide self-arching is difficult to justify where soil conditions are unknown and the degree of support provided by the bedrock cannot be quantified. What is more, the capacity of a soil arch to withstand overlying foundation loads is more difficult to assess than the span distance or arch thickness.  Small isolated foundations are probably the most vulnera­ble, and where the thickness of the arch is limited their failure probably occurs by punching shear. Larger more extensive and rigid foundations do have a greater ability to span open joints and to redistribute load.

Clay

Clay that has been strengthened by the addition of cement or lime can be used to fill large open joints in rock masses, being either compacted into place or used to help compact surface soil more effectively. The soil-cement arch method of foundation support is probably most suitable in those situations where the depth of superficial cover exceeds 3 m.  The degree to which the properties of a clay soil can be enhanced by the addition of cement or lime depends not only on the quantity added but also upon the type and proportion of clay minerals present.  In general, however, an increase in unconfined compressive strength of several hundred per cent can be obtained by the addition of a few per cent, by weight, of either cement or lime to a clay soil (a rough rule of thumb is 1.0% for every 10% of clay minerals present; rarely do clay soils contain more than 80% clay minerals).

Open joints and fissures

Open joints can be washed out and then filled with a grout material, although the grout mix does not need to be of an equivalent strength to that of the host rock mass. Cement, fly-ash and sand mixes can be used to fill joints. For example, gaping joints may be occupied with grouts consisting of one part cement, 3 to 5 parts fly-ash and 10 to 15 parts sand.  A small quantity of bentonite may be added to minimize segrega­tion of the grout. Gravel may be added to provide extra bulk when grout is used to fill widely gaping joints. Rock paste also may be used to fill joints.  It essentially consists of colliery spoil mixed with water.

For residential developments where joints opened by mining subsidence occurred beneath one or two metres of superficial deposits.  For example, where the site investigation revealed that an open joint occurred beneath a position in which a foundation structure was to be constructed, it was first exposed for a distance beyond the perimeter of the foundation equal to the depth of the backfill or to where it terminated, whichever was the least distance. Then, the open joint was filled with a bentonite grout and structural geowebbing was laid over the filled fissure (to accommodate any movement), after the initial set of the grout had taken place.  An impermeable membrane was laid over the geowebbing and turned up the face of the excavation for a distance of 350 mm.  The trench then was backfilled to foundation formation level with sand.  The latter was compacted in layers. Such treatment allowed strip footings to be adopted for both single and two-story dwellings.

Influence on groundwater

Longwall mining of coal gives rise to significant changes in the hydraulic properties and groundwater levels in overlying aquifers because of fracturing and bed separation associated with subsidence that, in turn, influence recharge, well yield and possible pollution. 

For instance an average fall in water level in wells in an unconfined aquifer of sand has been recorded in the Kamptee Coalfield, India.  This was attributed to the development of tensile strains of about 4.5 mm m^-1 caused by longwall mining of three panels of coal leading to an increase in the void space of the sand.  Unfortunately, this resulted in an acute shortage of water for irrigation and domestic use during the dry season.

The permeability of a sandstone aquifer in Jefferson County, in Illinois, USA, which is some 24 m thick, was observed to increase by one to two orders of magnitude and its storativity by one order, due to subsidence.  Well yields increased but the quality of the groundwater deteriorated, becoming more saline with higher sulphate content.  The potentiometric levels in the moderately transmissive sandstone declined rapidly during the tensional phase of subsidence but then partially recovered during the compressional phase.  The levels made a full recovery over several subsequent years.  By contrast, a sandstone of low transmissivity in Saline County, USA, experienced only slight increases in permeability due to fractures associated with subsidence.  The potentiometric levels in the sandstone declined rapidly and no significant recovery occurred.  It was concluded that the variations in hydrogeological properties, continuity and geometry of the hydrogeological units on a scale as local as a panel strongly affect the initial potentiometric response and critically control recovery.  What also should be borne in mind is that fractures opened by mining subsidence could act as pathways for contaminants that could affect aquifers at shallow depth. 

Boreholes were drilled in the Sherwood Sandstone (Triassic) prior to two panels being worked in the Barnsley coal seam, which is 2.5 m thick and occurs at a depth of 550 to 600 m in that part of the Selby Coalfield, North Yorkshire, England.  Pumping tests were carried out in the drillholes over a period of two years in order to determine the effects of subsidence on the hydrogeological properties of the sandstone.  The results indicated increases in the post-mining transmissivity of up to 234% directly over one of the panels and of up to 149% around the margins of the panels.  However, post-mining storativity remained largely unchanged.  More strikingly, the greatest effects were noticed during the closest approach of the second panel, which caused some additional subsidence over the first.  This gave rise to an increase in maximum transmissivity of 1979%, with increases in storativity of up to 625%.  This has been attributed the anomalous intra-cycle recovery-drawdown events that occurred during the latter phase as due to rapid dilation and compression of fractures in the aquifer associated with mining.  Although different behaviour patterns do occur in aquifers subjected to mining subsidence, the results obtained bear some similarities to those found in the United States mentioned in the previous paragraph.  However, the Barnsley seam is located at greater depth and so the investigation shows the subsidence effects still can influence the properties of shallow aquifers.

Overview of prediction methods of subsidence due to longwall mining

An important feature of subsidence due to longwall mining is its high degree of predictability. Usu­ally, movements parallel and perpendicular to the direction of face advance are predicted. Although adequate for many purposes such methodology does not consider the three dimensional nature of ground movement. For instance, observations have shown that individual points move on approxi­mately helical paths, that the pitch and radii change from point to point, and that the direction of rotation is dif­ferent on opposite sides of a subsidence basin.

Methods of subsidence prediction can be grouped into three fundamental categories. First, empirical methods attempt to fit subsidence functions to field measurements. Secondly, analytical or theoretical meth­ods of prediction derive subsidence functions from elastic theory and rock mechanics, and are based entirely on theory. Thirdly, semi-empirical methods develop subsidence functions based on theory but that are related to field data by the use of constants and correlation coefficients.

Empirical methods

Empirical methods of subsidence prediction such as those that were developed by the National Coal Board (NCB) (the Subsidence Engineers Handbook, 1975) were refined by continuous study and analysis of survey data from British coalfields. Unfortunately, however, empirical methods tend not to take topography, the nature of the strata and geological structure involved, and how the rock masses are likely to deform into ac­count.  Such empirical relationships can be applied only under conditions similar to those of the original observations. Never­theless, these methods are being improved continuously so that they can yield more accurate results. For example, the prediction methods developed by the NCB allow the amount of subsidence due to longwall mining in Britain to be predicted usu­ally within ± 10%.

Theoretical and numerical methods

The analytical or theoretical methods of subsidence prediction assume that stratal displacement behaves according to one of the constitutive equations of continuum mechanics over most of its range.  The continuum theories have been developed from the analysis of a displacement continuity produced by a slit in an infinite elastic half-space.  Analytical procedures subsequently were developed for three types of subsurface excavations based on elastic ground conditions that is, non-closure, partial closure and complete closure.  Further work extended the closed form solution to transversely isotropic ground conditions in both two and three dimensions.

Numerical models permit quantitative analysis of subsidence problems and are not subject to the same restrictive assumptions required for the closed form analytical solutions.  Finite element modelling frequently has been applied to subsidence problems since it can accommodate non-homogeneous media, non-linear material behaviour and complicated mine geometries.  Finite difference models can be used for the large strain, non-linear phenomena associated with subsidence development.  Other elastic approaches employing numerical techniques include boundary element methods. 

Semi-empirical methods

Most methods of subsidence prediction fall into the category of semi-empirical methods since fitting field data to theory often results in good correlations between predicted and actual subsidence.  There are two principal methods of semi-empirical prediction, namely, the profile functions and the influence func­tions methods.  The profile function method basi­cally consists of deriving a function that describes a subsidence trough.  The equation produced is nor­mally for one half of the subsidence profile and is expressed in terms of maximum subsidence and the location of the points of the profile.  In supercritical extraction the central position of the curve is Smax and changes to zero subsidence at the edges of the critical area. For sub critical extraction the profile is determined from the critical profile produced from an empirical/mathematical relationship.

Coal mining subsidence and its influence on building and structures

Ground movements

The different types of ground movement associ­ated with mining subsidence affect different buildings and struc­tures in different ways. For instance, vertical sub­sidence may seriously affect drainage systems, and tilt may cause serious concern as far as railways and tall structures, such as chimneys, are concerned. Damage to buildings generally is caused by differential horizontal move­ments and the concavity and convexity of the sub­sidence profile that give rise to compression and extension in the structure itself, the latter generally being the more serious. Usually, however, it is not just a simple matter of examining the reaction of a structure to a particular value of tensile or com­pressive strain.  For example, it is quite common for a structure to be subjected to compressive strains in one direction and tensile strains in another direc­tion.  It also may be subjected to alternative phases of tensile and compressive ground movements so there is a dynamic effect to consider.  Consequently, any acceptable design for a structure situated in an area of active longwall mining must have regard for the nature, degree and periodicity of the ground movements likely to be caused by mining.

Ground movement that adversely affects the safe­ty or function of a building or structure is unacceptable. How­ever, the appearance of many buildings is also of concern and therefore significant cracking of ar­chitectural features is unacceptable. Hence, an estimation of the amount of subsidence that will adversely affect structural members and/or archi­tectural features is required. This is influenced by many factors, including the type and size of the building or structure, and the properties of the materials of which it is constructed, as well as the rate and nature of the subsidence.  Because of the complexities in­volved, critical movements have not been deter­mined analytically. Instead, almost all criteria for tolerable subsidence or settlement have been estab­lished empirically on the basis of observations of ground movement and damage in existing buildings.

Total displacement of a structure may be regarded as consisting of five components, three of which are rigid body displacements, the remaining two being distortional components.  The latter components are consequent on divergences within the structure from uniform movements and represent the main causes of damage.

As far as the effects of subsidence on buildings or structures are concerned, it should not be assumed that ground movements produced in the presence of buildings or structures are the same as those when a they are absent.  Moreover, although in many cases the contact between the ground and building or structure is maintained during the period of ground movement, in some situations gaps develop between the ground and building or structure, and slip type displacements may take place.  Friction and adhesion at the interface between the ground and foundation structure during subsidence generate structural deformation equal to at least a fraction of the horizontal displacement.  The strength of structural components may be high enough to withstand damage when the ground strains are compressive but this may not be the case when the ground undergoes tensile strain. 

Horizontal displacements

The horizontal displacements of a foundation structure and the ground located in the zone of tension are compatible as long as the shear stresses along the interface between the two are less than the shear strength of the interface.  If the latter is exceeded, then slippage occurs along the underside of the foundation structure.  The ground-structure interaction also is influenced by the fact that buildings or structures are not perfectly flexible, hence the magnitude of vertical support reaction may vary during the passage of a subsidence wave.  As noted above, discontinuities may concentrate ground strain and so a building or structure founded above such a feature may be damaged even though the horizontal strain over the length of the building or structure was rather modest.

Differential settlement

Two parameters commonly have been used for developing correlations between damage and dif­ferential settlement, namely, angular distortion and deflection ratio. Angular distortion, d/l, is the differential movement between two points divided by the distance separating them.  When re­lated to building damage, angular distortion com­monly is modified by subtracting the rigid body tilt, w, from the measured displacement.  In this way the modified value is more representative of the de­formed shape of the building.  The deflection ratio, D/L, is defined as the maximum displacement, D, relative to a straight line between two points divided by the distance, L, separating the points. An­gular distortion (relative rotation) may be used as the critical index of ground movement. Cracking of load bearing walls or panel walls in frame structures is likely when d/l exceeds 1/150.

Tilting

Tilting is the rigid body rotation that does not contribute to the distortion of the structure.  Hence, both removed the differential movement due to tilting from the computed values of angular distortion.  However, in the case of framed structures supported on isolated spread foot­ings, the validity of this assumption is question­able.  In such a case, tilting con­tributes to the stress and strain in the frame unless each footing tilts or rotates through the same angle as the overall structure.  Because this is unlikely to occur the effects of tilt should be included in the differential movement criteria.

Angular distortion

The use of angular distortion as a criterion of structural damage has been criticized as an oversim­plification, it being argued that the effect of ground curvature and type of structure was not fully ap­preciated.  This is particularly the case in relation to the behaviour of load bearing brick walls undergoing hogging or sagging.  What is more, angular distortion implies that damage is due to shear distortion within the structure, which is not necessarily the case.

Deflection ratio

Allowable dis­placement may be defined in terms of deflection ratio, D/L. The allowable displacement for frames is expressed in terms of the slope or the differential displacement between adjacent columns.  This is very similar to the angular distortion without correction for tilt. 

Differential ground movements

When differential ground movement occurs, a building or structure may undergo both distortion and tilt.  In the case of tall structures, the large height to length ratio generally gives rise to a predominantly rigid body rotation, although some distortion may occur. In fact, tilt may lead to some tall structures collapsing.  On the other hand, when low-rise buildings are subjected to differential subsidence, then distortion normally is of more concern than tilt.  When low-rise buildings in areas of mining subsidence have been constructed on rafts with adequate stiffness to resist horizontal tensile forces, then differential subsidence causes buildings to tilt as a rigid body, and in this way prevents distortion of the building and cracking of walls.  Nonetheless, there comes a point when tilt becomes unacceptable in terms of aesthetics, serviceability (e.g. doors swinging open, drainage falls becoming insufficient etc) or stability. The tolerability of tilt depends on the type of building and the purpose it serves.

Classification of damage

Criteria for subsidence damage to buildings propose recognized three classes of damage, namely, architectural that was characterized by small scale cracking of plaster and doors and windows sticking; functional damage that was characterized by instability of some structural elements, jammed doors and windows, broken window panes, and restricted building services; and structural damage in which primary structural members were impaired, there was a possibility of collapse of members, and complete or large-scale rebuilding was necessary.  Basements may be considered the most sensitive parts of houses with regard to subsidence damage, and therefore that basements usually suffered more damage than the rest of a building.

National Coal Board classification

Investigations carried out by the National Coal Board have revealed that typ­ical mining subsidence damage starts to appear in conventional structures when they are subjected to effective strains of 0.5 to 1.0 mm m^-1 and damage can be classified as negligible, slight, appreciable, severe and very severe. However, this re­lationship between damage and change in length of a building or structure is only valid when the average ground strain produced by mining subsidence is equalled by the average strain in the building or structure.  In fact, this commonly is not the case, strain in the structure being less than it is in the ground. This method only serves as a guide to the likely damaging effects of ground strains induced by mining subsidence.  In addition, it takes no account of the design of a building or structure, or of construction ma­terials.  Nevertheless, it indicates that the larger a building or structure, the more susceptible it is to differential vertical and horizontal ground movement.

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