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Unusual cases of mining subsidence from Great Britain, Germany and Colombia
Abstract
Subsidence involves sinking of the ground surface. The movement generally is localised and may or may not involve some amount of horizontal movement. It may be rapid or take place gradually over a period of time. Subsidence may be brought about by natural causes as, for example, when the roof of a cavern in limestone is weakened to the extent that it is no longer self-supporting and so collapses. Other more exotic examples are associated with volcanism and earthquakes. Perhaps, however, subsidence is more frequently associated with movements caused by mining activities, that is, the removal of mineral deposits, be they in solid, liquid or gaseous form, from within the ground. Mining is one of the earliest activities of man and has taken place in every continent. Subsidence also can result from subsurface excavations such as tunnels, caverns, cellars and sewers. One of the added problems of some forms of subsidence is that it is impossible to predict. This, coupled with the fact that the presence of potentially collapsible voids may be unknown, unrecorded or simply forgotten about further complicates the problem. The objectives of this paper are to document and draw attention to a number of unusual examples of subsidence. These have been generated due to the mining of chalk in southern England, the collapse of slate mines and caverns in Germany, the underground extraction of evaporites in Northern Ireland, fault reactivation in Wales and northern England and the extensive extraction of pumice on the flanks of Galeras volcano in Colombia.
... The European Ground Motion Service [24] has played a pivotal role in advancing the accessibility of Sentinel-1 data, thereby integrating radar images into standard monitoring routines for land subsidence. Specifically, it has facilitated the examination and analysis of land subsidence processes across various mining regions worldwide, including Belgium [25,26], Colombia [27], China [28,29], the Czech Republic [30], the United Kingdom [27,31], the Netherlands [32], Germany [19,20,27,31,[33][34][35], Poland [36][37][38], and the Republic of South Africa [31]. Red arrows indicate the mining damage. ...
... The European Ground Motion Service [24] has played a pivotal role in advancing the accessibility of Sentinel-1 data, thereby integrating radar images into standard monitoring routines for land subsidence. Specifically, it has facilitated the examination and analysis of land subsidence processes across various mining regions worldwide, including Belgium [25,26], Colombia [27], China [28,29], the Czech Republic [30], the United Kingdom [27,31], the Netherlands [32], Germany [19,20,27,31,[33][34][35], Poland [36][37][38], and the Republic of South Africa [31]. Red arrows indicate the mining damage. ...
... The European Ground Motion Service [24] has played a pivotal role in advancing the accessibility of Sentinel-1 data, thereby integrating radar images into standard monitoring routines for land subsidence. Specifically, it has facilitated the examination and analysis of land subsidence processes across various mining regions worldwide, including Belgium [25,26], Colombia [27], China [28,29], the Czech Republic [30], the United Kingdom [27,31], the Netherlands [32], Germany [19,20,27,31,[33][34][35], Poland [36][37][38], and the Republic of South Africa [31]. Red arrows indicate the mining damage. ...
Direct and indirect effects after mine operations cease operating must ideally be subjected to perpetual monitoring routines in order to detect possible risks or avoid adverse effects on the surrounding ecosystems at an early stage. In this contribution, mining subsidence lakes created inside the nature reserve Kirchheller Heide and Hilsfeld Forest are subjected to analysis for a long-term monitoring scheme. For this purpose, we employ high-resolution unmanned aerial system (UAS)-based multispectral and thermal mapping tools to provide a fast, non-invasive and multitemporal environmental monitoring method. Specifically, we propose to monitor vegetation evolution through multispectral analysis, biotypes identification using machine learning algorithms, and water surface extent detection, together with their thermal behavior. The aim of this contribution is to present the proposed workflow and first results to establish a baseline for future analyses and subsequent surveys for long-term multi-temporal monitoring.
... Kretschmann [2] refers to the monitoring of mining activities as a perpetual task due to the long-term nature of the issue. The literature describes the effects of land subsidence in mining areas from: Belgium [52,53], Columbia [51], China [54,55], Czech Republic [56], United Kingdom [50,51], Netherlands [57], Germany [33,48,50,51,[58][59][60], Poland [61][62][63] and Republic of South Africa [50]. ...
... Kretschmann [2] refers to the monitoring of mining activities as a perpetual task due to the long-term nature of the issue. The literature describes the effects of land subsidence in mining areas from: Belgium [52,53], Columbia [51], China [54,55], Czech Republic [56], United Kingdom [50,51], Netherlands [57], Germany [33,48,50,51,[58][59][60], Poland [61][62][63] and Republic of South Africa [50]. ...
... Kretschmann [2] refers to the monitoring of mining activities as a perpetual task due to the long-term nature of the issue. The literature describes the effects of land subsidence in mining areas from: Belgium [52,53], Columbia [51], China [54,55], Czech Republic [56], United Kingdom [50,51], Netherlands [57], Germany [33,48,50,51,[58][59][60], Poland [61][62][63] and Republic of South Africa [50]. ...
Direct and indirect effects after mine operations cease must ideally be subject to perpetual monitoring routines in order to detect possible risks or avoid adverse effects on the surrounding
ecosystems at an early stage. In this contribution, mining subsidence lakes created inside the nature reserve Kirchheller Heide and Hilsfeld Forest are subjected to analysis for a long-term monitoring scheme. For this purpose, we employ high-resolution unmanned aerial system (UAS)-based multispectral and thermal mapping tools to provide a fast, non-invasive and multitemporal
environmental monitoring method. Specifically, we propose to monitor vegetation evolution through multispectral analysis, biotypes identification using machine learning algorithms, and
water surface extent detection, together with their thermal behavior. The aim of this contribution is to present the proposed workflow and first results to establish a baseline for future analyses and subsequent surveys for longterm multi-temporal monitoring
... Abandoned shallow mines can be a serious problem in areas under development or redevelopment. Bell et al. [18] drew attention to a number of unusual examples of subsidence, including one caused by gypsum mining in southern England, the collapse of slate mines and caverns in Germany, underground evaporite mining in Northern Ireland, and the extensive pumice mining on the flanks of the Galeras volcano in Colombia. ...
Coniolo and Brusaschetto, are two small towns located in the Monferrato area of the Alessandria Province, northern Italy. These communities have similar histories related to development and subsequent abandonment of marl quarry activity that began more than a century ago and continued until recently. Quarrying occurred until soil conditions, water infiltration, and excessive depth made cost of extracting and7 lifting material prohibitive. Quarries consisted of tunnels located directly beneath the towns at about 150 m below ground surface. Collapse of the tunnels led to surface subsidence and destruction of overlying homes and much of the municipal infrastructure. In the early Twentieth Century, regulations pertaining to mine and quarry safety were typically deficient, entirely absent, or not followed. Extractive activities of non-energy mineral resources from quarries and mines were and continue to be widespread in Italy, which currently ranks fifth among what are now countries of the European Union (EU). Mining sites are present in all regions of Italy, particularly in the northern part of the country and along coasts, often in areas of geohydrogeological risk. Consequences of anthropogenic pressures that alter the natural environment, such as the physical size of aquifer drawdowns, are linked to issues for a number of extractive sites across the country. This report analyzes historical and technical documents, conducts a geomorphological analysis of hilly slopes surrounding these communities, and examines urban planning and geophysical surveys to determine the impact of subsurface quarrying activities on the overlying ground surface. The study highlights significant problems that are applicable to other localities globally. This research demonstrates: (a) the importance of geological considerations to development and abandonment of mining activity in inhabited areas; (b) the importance of establishing and following safety protocols; and (c) the manner in which economic interests can take precedence over the well-being and lives of those employed to extract resources.
... The physical and mechanical properties of backfill materials and the technique of monitoring and ensuring performance are necessary to control and perform the filling [3]. The physical, chemical, and mechanical properties of different mixtures were studied and their impact on obtaining the best, cheapest, and strongest suitable mixture of backfill materials for the selection and systematic application of backfill in underground mines [7,8]. ...
Backfilling material such as tailing (mine wastes) mixing with cement or gypsum has grown throughout the world’s underground mines. However, despite their growing popularity, the typical hydraulic and mechanical fill types utilized in many mines still exist. Deep underground mining has increased due to the lack of commercial minerals nearby. Mine wastes were considered the main part of backfilling to prevent environmental pollution, ground subsidence after mine abandonment, and mine collapse during deeper extraction phases. The cemented backfill technique is the principal technique used in underground mines, which include cement with fly ash and/or filter dust, cement with tailing material and fly ash, gypsum with fly ash, and synthetic anhydrite with fly ash and have been reviewed. It has concluded that a backfilling material must be selected based on further goals, available material near the mine site, and economic factors. This paper analyzes different backfill material mixtures to create a technique that will increase safety in underground mining conditions and foresees an appropriate formula that gives high uniaxial compressive strength. The multiple linear regression (MLR) on the collected data from the experimental works to construct the relationship between the uniaxial compressive strength (UCS) of the mixture and the components of the backfilling and the prediction formula for expected compressive strength was obtained. The results revealed that the predicted regression equation was robust and reliable to predict the (UCS) for the new components of the filling (cement (CE), filter dust (FD), water content (WC), and time (T)).
... One of the main issues in many parts of the world is represented by the subsidence induced by underground mining (Villegas et al. 2011;Zhou et al. 2015;Przyłucka et al. 2015a, b;Vu Khac et al. 2021). Such effects are more harmful when the activities legal or not authorized are in correspondence or nearby urban areas (Bell et al. 2005;Prakash et al. 2010;Ji et al. 2011;Villegas et al. 2011;Marschalko et al. 2012). Subsidence can either coincide with mining activities or be delayed in response to the time-dependent deformation of rocks. ...
Underground mining can produce subsidence, which can be coincident with mining activities or delayed in response to the time-dependent deformation of the rocks. Therefore, in these cases, it is essential to effectively monitor the soil deformations at different times during and after mining activity. In the present work, an integrated approach based on geotechnical numerical modeling and Advanced Differential Interferometric Synthetic Aperture Radar (A-DInSAR) method has been applied to detect, study and monitor the subsidence related to mining activity in the Nuraxi Figus coal district (Sardinia, Italy). Two datasets of high-resolution COSMO-Skymed images were acquired, respectively in two covering periods: from 2011 and 2014, and from 2013 to 2020. The A-DInSAR results show that the predominant displacement rates are located in correspondence with the panels. The cumulated satellite-based LoS displacements vary in the first period between − 130 and + 28 mm and − 293 and + 28.4 mm, while, during the second period between − 6.9 and + 1.6 mm and − 8.72 and + 4.33 mm in ascending and descending geometries, respectively. The geotechnical numerical model allowed to obtain a value for the maximum expected. By using the vertical and horizontal components it was possible to reconstruct the kinematics of the deformation considering three phases: pre-mining, syn-mining, and post-mining activity. The temporal evolution of displacements started during the mining extraction in 2011, achieved the major values in correspondence of post-mining operations, during the period from 2013 to 2014 and continued slowly until 2020. The near real-time monitoring system applied in this study proved to be very useful for detecting subsidence during the mining activity and the post-mining period.
... In the case of mining, the heterogeneous rock mass with geological discontinuities affects stress redistribution. Therefore, the ground subsidence can be influenced [5,93,94]. In addition, there have been no earthquakes in Laizhou City since 2018 according to the earthquake data. ...
Ground subsidence is a common geological phenomenon occurring in mining areas. As an important Chinese gold mine, Sanshandao Gold Mine has a mining history of 25 years, with remarkable ground subsidence deformation. Mining development, life security, property security and ecological protection all require comprehension of the ground subsidence characteristics and evolution in the mining area. In this study, the mining subsidence phenomenon of the Sanshandao Gold Mine was investigated and analyzed based on Persistent Scatterer Interferometry (PSI) and small baseline subset (SBAS). The SAR (synthetic aperture radar) images covering the study area were acquired by the Sentinel-1A satellite between 2018 and 2021; 54 images (between 22 February 2018 and 25 May 2021) were processed using the PSI technique and 24 images (between 11 April 2018 and 12 July 2021) were processed using the SBAS technique. In addition, GACOS (generic atmospheric correction online service) data were adopted to eliminate the atmospheric error in both kinds of data processing. The interferometric synthetic aperture radar (InSAR) results showed a basically consistent subsidence area and a similar subsidence pattern. Both InSAR results indicated that the maximum LOS (line of sight) subsidence velocity is about 49 mm/year. The main subsidence zone is situated in the main mining area, extending in the northwest and southeast directions. According to the subsidence displacement of several representative sites in the mining area, we found that the PSI result has a higher subsidence displacement value compared to the SBAS result. Mining activities were accompanied by ground subsidence in the mining area: the ground subsidence phenomenon is exacerbated by the increasing mining quantity. Temporally, the mining subsidence lags behind the increase in mining quantity by about three months. In summary, the mining area has varying degrees of ground subsidence, monitored by two reliable time-series InSAR techniques. Further study of the subsidence mechanism is necessary to forecast ground subsidence and instruct mining activities.
... Furthermore, several studies have also focused on ground movement associated with fault activation. Bell et al. (2005) reported mining subsidence from Great Britain, Germany and Colombia, and stated that mining area experiencing reactivation of faults should be surveyed properly before construction and a safe gap of at least 10 m should be maintained between the fault zone's edge and any structures. Moreover, Mohammady et al. (2019) employed Random Forest theory to analyse subsidence susceptibility and found that gap from the fault, elevation, slope angle and water table had the largest influence on ground deformation. ...
Underground coal mining activities and ground movement are directly correlated, and coal mining-induced ground movement can cause damage to property and resources, thus its monitoring is essential for the safety and economics of a city. Fangezhuang coal mine is one of the largest coalfields in operation in Tangshan, China. The enormous amount of coal extraction has resulted in significant ground movement over the years. These phenomena have produced severe damages to the local infrastructure. This paper uses the finite difference method (FDM) 3D model and the stacking interferometric synthetic aperture radar (InSAR) method to monitor the ground movement in Fangezhuang coalfield during 2016. The FDM 3D model used calibrated Fangezhuang geological parameters and the satellite InSAR analysis involved the use of ascending C-band Sentinel-1A interferometric wide (IW) data for 2016. The results show that the most prominent subsidence signal occurs in mining panel 2553N and the area between panel 2553N and fault F0 with subsidence up to 57 cm. The subsidence observed for the FDM 3D model and stacking InSAR to monitor land deformation under the influence of fault are in close agreement and were verified using a two-sample t-test. It was observed that the maximum subsidence point shifted towards the fault location from the centre of the mining panel. The tectonic fault F0 was found to be reactivated by the coal mining and controls the spatial extent of the observed ground movement. The impact of dominant geological faults on local subsidence boundaries is investigated in details. It is concluded that ground movement in the study area was mainly induced by mining activities, with its spatial pattern being controlled by geological faults. These results highlight that the two methods are capable of measuring mining induced ground movement in fault dominated areas. The study will improve the understanding of subsidence control, and aid in developing preventive measures in Fangezhuang coalfield with fault reactivation.
One of challenges of today’s world is the long-term geo-monitoring of phenomena and processes that affect our environment after the closure of mining activities. Water resources are one of the components affected by post-mining processes. Moreover, land subsidence can be observed both during and after the cessation of mining activities. This phenomenon has an impact on the entire water management of a region. So far, radar or multispectral images have been used to identify water surfaces. This paper will present a methodology for using drones to detect water surfaces using vegetation indices such as NDVI, GRNDVI and NDWI. During their research, the authors modified the GRNDVI indicator by including the Red Edge band in the calculations. The newly developed Green Red Water Index – GRWI, makes it possible to identify water surfaces. This is important, because the change of water conditions makes it important focus more on the water supply and availability. However, analysis of the spectral bands of the different land-use classes in the Ruhr study area shown that the spectral profiles for water, soils, road and street surfaces have similar spectral characteristics and therefore difficulties may arise in distinguishing between the land-use classes shown. In this article a comparison of the indicators will be presented: NDVI, GRNDVI, NDWI and GRWI together with their statistical interpretation.
Ground subsidence is a pervasive feature of landscapes. There are many processes that cause it: changing groundwater conditions, solutional collapse of salt and gypsum, coal and salt mining, the abstraction of hydrocarbons, geothermal fluid abstraction, shrinkage of organic soils and peats, and hydrocompaction. Subsidence can be associated with enhanced seismic activity and the formation of ground fissures.
Physical factors likely to affect the genesis of the various fault rocks-frictional properties, temperature, effective stress normal to the fault and differential stress-are examined in relation to the energy budget of fault zones, the main velocity modes of faulting and the type of faulting, whether thrust, wrench, or normal. In a conceptual model of a major fault zone cutting crystalline quartzo-feldspathic crust, a zone of elastico-frictional (EF) behaviour generating random-fabric fault rocks (gouge-breccia- cataclasite series-pseudotachylyte) overlies a region where quasi-plastic (QP) processes of rock deformation operate in ductile shear zones with the production of mylonite series rocks possessing strong tectonite fabrics. In some cases, fault rocks developed by transient seismic faulting can be distinguished from those generated by slow aseismic shear. Random-fabric fault rocks may form as a result of seismic faulting within the ductile shear zones from time to time, but tend to be obliterated by continued shearing. Resistance to shear within the fault zone reaches a peak value (greatest for thrusts and least for normal faults) around the EF/QP transition level, which for normal geothermal gradients and an adequate supply of water, occurs at depths of 10-15 km.
This area to the N and S of Belfast Lough has mainly Palaeozoic rocks in County Down, with Mesozoic strata and Tertiary volcanic rocks in County Antrim. The Ordovician rocks are mainly sub-greywackes and locally contain clastic grains of glaucophane or crossite. The Lower Carboniferous sandstones, shales and siltstones include numerous thin evaporite replacement beds in the upper part of the sequence. The Triassic sandstones, mudstones and marls are succeeded by poorly exposed Lower Lias mudstones. The Cretaceous sediments comprise the Hibernian Greensands formation and the Ulster White Limestone formation. The Tertiary igneous rocks are dominated by basalt flows but trachytes are also reported. The intrusive rocks include dolerite dykes and, at Carneal, a dolerite plug intruded through the lavas which has dragged up a screen of highly metamorphosed chalk (M.A. 76-2124, 83M/0514). As a result of contamination by the chalk, the dolerite has developed hybrid pyroxenite and titanaugite-melilite rocks while the metamorphism and metasomatism of the chalk has given a suite of calc-silicate rocks, including a larnite-magnetite rock containing gehlenite (M.A. 82M/3222). -R.A.H.
Fault scarps and graben features indicative of slope deformation have been observed adjacent to the rear scarps of landslides and on moorland plateaux in the Pennines. The scarps are distinct, up to 2 m high and can be traced for a maximum distance of approximately 400 m. These severely reduce the strength of the rock mass, enable groundwater to be channelled onto the upper valley slopes and may have played an important role in the initiation of first-time slope failures, and in the reactivation of older landslides. These features are similar to those recently described on the interfluves of the South Wales Coalfield valleys, and are consistent with those described as 'block movements' elsewhere in the world. Those in South Wales have been interpreted, by some previous investigators, as being generated during mining subsidence. However, in the Pennines, the slope and plateaux movements occur in the Namurian (Upper Carboniferous) sedimentary sequences where there has been no mining and it is therefore evident that other mechanisms are involved. In both South Wales and the Pennines steep-sided valleys have incised the moorland plateaux which in both cases are capped by strong, well-jointed cap rocks. These have exposed the underlying, much weaker, fissile mudstones which form the middle and lower slopes. These block movements in the Pennines are documented, discussed and compared with those in South Wales.
The North Staffordshire Coalfield occupies the northern apex of a triangular area of late Proterozoic continental crust, the Midlands Microcraton. Most faults identified at surface in the late Carboniferous rocks originated either as a result of reactivation of structure during the Variscan orogen in the late Carboniferous, or its collapse in the early Permian. The coalfield has been extensively undermined and many examples of mining-induced fault movement have been recorded in the Barlaston area between 1960-2000. The style of ground deformation observed in the area is described. Most movements have resulted in a series of distinct, extensive, fault scarps and fissures on the ground surface, causing widespread damage to structures, property, underground utilities and land. Several phases of fault movement have occurred, separated by periods of relative stability. Fault scarps may occasionally reach 2 m high, being indicative of multi-seam (3+) mining operations. These are restricted to a few metres in width but reach several hundreds of metres in length. The reasons why so many faults have been reactivated around Barlaston, why the surface expression of the faults are different in Carboniferous and Triassic outcrops, and why some faults appear to have reactivated since the cessation of mining are discussed.
Davis cites four areas of low-angle faulting in which he believes that high fluid pressures can have played no important part in the development and movement of the thrust plates, but it seems to us that the concept or some variant of it may help to explain the observed field relationships in the three out of these four areas with which we have had some first-hand experience. In the areas of the Heart Mountain thrust of Wyoming, the Muddy Mountain thrust of Nevada, and the structurally higher, crystalline thrust sheets of the Swiss Alps, field relationships which include evidence of dehydration reactions during metamorphism of evaporites and of pelitic rocks suggest that interstitial fluid pressures may have been high and thus have played an essential part in the development of the thrust faults. In the fourth area cited by Davis, that of his own studies in the Klamath Mountains of California, we have had no first-hand experience and thus are not competent to answer his criticisms.
Soluble carbonate rocks often pose a subsidence hazard to engineering and building works, due to the presence of either metastable natural solution features or artificial cavities. There is also an inherent danger to the public and lives have been lost because of unexpected ground collapses. Although site investigation techniques are becoming increasingly elaborate, the detection of hazardous ground conditions associated with limestones is frequently difficult and unreliable. Remedial measures to solve subsidence problems following foundation failure are expensive. It would be advantageous if areas liable to subsidence could be identified in a cost-effective manner in advance of planning and ground investigation. Hazard mapping could then be used by planners when checking the geotechnical suitability of a proposed development or by engineering geologists/geotechnical engineers to design the type of ground investigation best suited to the nature and scale of the potential hazard.
Recent research focussed on the English Chalk outcrop has led to the development of two new models to predict the subsidence hazard for both natural solution features and artificial cavities. The predictive models can be used to map the hazard at any given chalkland locality, as a cost-effective precursor to ground investigation. The models, although created for the Chalk outcrop, have important implications for all types of limestone terrain.
The basis of the predictive modelling procedure is an analysis of the spatial distribution of nearly 1600 natural solution features, and more than 850 artificial cavity locations, identified from a wide varietyy of sources, including a special appeal organized by CIRIA. A range of geological, hydrogeological and geomorphological factors are evaluated to identify significant relationships with subsidence. These factors are ranked, numerically weighted and incorporated into two quantitative subsidence hazard model formulae. The models can be applied to perform hazard mapping.
A sudden subsidence under a footpath which led to the tragic death of a pedestrian was followed by a series of further subsidences over a period of several years, all incidents apparently located within an area no more than approximately 1 km square. The area is one of high density housing of the terraced style which was largely developed in the period 1900-1940. Further housing estates have been added in the period since the 1950s.
Increasing public concern over the incidents led to the commissioning of a preliminary study by the Rochester-upon-Medway City Council to collate and assess relevant archival information to determine whether the subsidence occurrences in the area could be related to some common cause. The study included reference to local museums, libraries and societies, visits to the British Library Map Department, a review of the geological literature and a collation of the industrial history of the area. Several potential causes of subsidence were discovered; these included the existence of old water wells and dene holes and, more significantly, extensive excavations associated with brick production at the turn of the century. In addition, a canal had been tunnelled under the area in 1823, subsequently partly infilled and converted to railway use.
The probable cause of the incidents at Frindsbury has been attributed to the existence of chalk mines associated with the brickfields and further investigation is now taking place to locate these.
Clues to all of the features discussed above were available as open file information in public records. This paper describes how the information was acquired and assimilated and emphasizes the importance of the role of desk study in the initial stages of any development project.
Promise of resolving the paradox of overthrust faulting arises from a consideration of the influence of the pressure of interstitial fluids upon the effective stresses in rocks. If, in a porous rock filled with a fluid at pressure p, the normal and shear components of total stress across any given plane are S and T, then are the corresponding components of the effective stress in the solid alone.
According to the Mohr-Coulomb law, slippage along any internal plane in the rock should occur when the shear stress along that plane reaches the critical value where σ is the normal stress across the plane of slippage, τ0 the shear strength of the material when σ is zero, and ϕ the angle of internal friction. However, once a fracture is started τ 0 is eliminated, and further slippage results when
This can be further simplified by expressing p in terms of S by means of the equation which, when introduced into equation (4), gives
From equations (4) and (6) it follows that, without changing the coefficient of friction tan ϕ, the critical value of the shearing stress can be made arbitrarily small simply by increasing the fluid pressure p. In a horizontal block the total weight per unit area Szz is jointly supported by the fluid pressure p and the residual solid stress σzz; as p is increased, σzz is correspondingly diminished until, as p approaches the limit Szz, or λ approaches 1, σzz approaches 0.
For the case of gravitational sliding, on a subaerial slope of angle θ where T is the total shear stress, and S the total normal stress on the inclined plane. However, from equations (2) and (6)
Then, equating the right-hand terms of equations (7) and (8), we obtain which indicates that the angle of slope θ down which the block will slide can be made to approach 0 as λ approaches 1, corresponding to the approach of the fluid pressure p to the total normal stress S.
Hence, given sufficiently high fluid pressures, very much longer fault blocks could be pushed over a nearly horizontal surface, or blocks under their own weight could slide down very much gentler slopes than otherwise would be possible. That the requisite pressures actually do exist is attested by the increasing frequency with which pressures as great as 0.9Szz are being observed in deep oil wells in various parts of the world.
