mechanics of upward propagation of cover collapse sinkholes cover collapse sinkholes occur by failure of the walls of a soil void above cavernous bedrock i examine conditions for failure in compression by crack propagation and coalescence and for failure by sloughing in which pore water pressure produces a net tension perpendicular to the wall of the void compressive failure without relaxation of stress does not explain observed long term stability of thick soils nor failures in thin residual soils if stress relaxation occurs with compressive failure soil voids tend to stabilize and sinkholes are not predicted sloughing failure is not predicted for steady state pore pressure fields even for a perched water table at the surface over a drained void transient pore pressure conditions that could produce sloughing may result from 1 rapid drawdown causing soil consolidation and transient high pore pressure gradients 2 approach of a wetting front in unsaturated soil with high permeability behind the front 3 dissolution of air from bubbles in the soil and exsolution near the void producing a low permeability zone near the void

prediction of undrained sinkhole collapse sinkholes are surface depressions or shafts resulting from the collapse of a submerged cavity in soil the cavities that lead to sinkholes form as a result of underlying geology in limestone areas or as a result of human activity such as mining or leakage from a sewer the formation of sinkholes is often sudden and can lead to extensive damage and loss of life especially in urban areas much of the literature on the subject of sinkhole formation is empirical in nature often being associated with specific locations this paper presents the results of a study using numerical modeling of the undrained stability of the submerged cavities that lead to sinkhole formation finite element limit analysis techniques using programs developed at the university of newcastle are used to obtain upper and lower bound values of a suitable load parameter which bracket the exact solution the results are compared to analytical solutions both from literature and derived independently

divergent and convergent non isochoric deformation plane strain flow with zero elongation parallel to but widening or shortening perpendicular to the flow plane results in either divergent or convergent non isochoric deformation during this special type of flow the kinematic dilatancy number a measure of the rate at which a surface changes area with time is directly dependent on the kinematic vorticity number a measure of the rotational quality of a flow type and vice versa thus the velocity gradients tensor can be simplified being only defined by the vorticity and the instantaneous area change if these numbers can be deduced from natural deformed rocks with the help of quantitative kinematic indicators the finite deformation can be calculated if the volume change is known from independent criteria we quantitatively examine a marble mylonite from the tauern window which deformed by stress induced solution mass transfer that exhibits convergent non isochoric deformation

state of strain in a quartzite mylonite central australia abstract the finite strain due to mylonitization of a quartzite has been determined using measurements of deformed quartz grains and ribbons developed from quartz grains equant before the deformation the mylonites are developed in long narrow steeply dipping mylonite zones within the chewings range quartzite of central australia this quartzite is very pure 98 quartz the quartzite surrounding the mylonite zones appears unstrained the samples examined exhibit severe flattening strains k values of between 0 01 and 0 12 and r values of between 5 and 30 have been determined application of formulae to calculate volume change assuming the model of an ideal ductile deformation band structure indicate significant apparent volume losses with values between 0 69 and 0 95 such values seem unreasonably high as no geological evidence for large volume loss is seen the band structure model is considered inapplicable for these mylonite zones the observed structural features can best be explained by a deformation history involving severe bulk shortening normal to the zones

designing foundations around sinkholes there is an increasing awareness among developers and owners of the need to conduct subsurface exploration studies before planning a project the use of geophysical methods in subsurface exploration has been established to be valuable in locating sinkhole activity and suggesting pro active measures however the value of geophysical exploration to supplement geotechnical investigation has not yet been stressed primarily out of cost concerns ground penetrating radar and electrical resistivity tests which were used to determine void spaces below proposed buildings are gaining wider acceptance as a result of information obtained from geophysical tests foundation designs were modified to use post tensioned mats or to include grouting an improved grouting technique that controls the volume of grout being pumped is also discussed this paper is an attempt to document some case studies which resulted in making design improvements to mitigate the effects of known sub surface solution activity these case studies illustrate the use of geophysical exploration methods in adding value to the engineered design

models of strain variation in nappes and thrust sheets a review abstract strain within nappes and thrust sheets can be modelled using simple boundary conditions an original rectangular prism of material resting on a thrust plane is considered to be subject to various pure and simple shear components operating parallel to the thrust deformation gradient tensors are determined for the models and solutions found for the principal strains a two dimensional model considers heterogeneous simple shear combined with a stretch in the direction of shear simple shear zones arise as a special case where 1 recumbent fold nappes characteristic of gravitational collapse can be modelled with 1 and thrust sheets with layer parallel shortening and folding with differential transport of nappes gives rise to additional wrench type shears solutions for the principal strains in this type of model are found and used to interpret side wall ramps and steep zones parallel to nappe movements by including a stretch in the transport direction these differential transport models produce prolate strains 1 and oblate strains finally a brief consideration of bending strains produced in a sheet passing over a ramp indicates reversals in the shear direction during the strain history these predict possible crenulation of early thrust fabrics at ramps

calculation of volume change in ductile band structures abstract volume changes incurred during the development of ideal band structures infinite shear zones can be readily calculated if one knows the principal directions and principal ratios of total strain within and adjacent to the ideal band structures the calculation is greatly simplified if one knows the directions and ratios of the strain that generated the band structures or if the total strain of the host rocks is zero in some natural deformation zones apparent volume losses according to the band model exceed 30 and may be unreasonably high further determinations of apparent volume change will help to judge the physical viability of the band model and its strict geometrical requirements for example the propagation of embryonic deformation zones may lead to total strain patterns that differ greatly from those of band structures

strain analysis of a northern apennine shear zone using deformed marble breccias abstract the alpi apuane region of the northern apennines appears to have been deformed within a large scale low angle shear zone with an overthrust sense of movement the presence of mineral stretching lineations folds progressively rotated into the x strain direction and schistosities which intersect the nappe boundaries at small angles suggest that a component of shear strain occurred during the deformation the strain ratios and orientations on two dimensional sections have been determined from deformed marble breccias reduction spots and oncalites data from three or more non perpendicular non principal sections have been combined to determine the finite strain ellipsoids at 33 sites within the shear zone the finite strains have been separated into components of simple shear longitudinal strain and volume change algebraic expressions have been derived and graphs constructed which enable components of and and and to be determined directly from a knowledge of strain ratio r within the shear zone and the angle between the principal strain direction and the shear zone boundary the alpi apuane data indicate that neither simple shear alone nor simple shear with volume change can satisfactorily explain the observed strains consideration of simple shear plus longitudinal strain leads to a general relationship in which the value of shear increases and the values of longitudinal strain change along a sw ne profile across the zone integration of the resulting shear strain distance curves gives a minimum displacement of 4 km within the shear zone combination of the finite strains with the total time of deformation known from k ar studies leads to average strain rates from 1 4 to 9 6 10 15 sec 1 a characteristic flat ramp flat geometry initially formed the boundaries of what was later to develop into the overthrust shear zone and deformation of the underlying crystalline basement is believed to have occurred by ductile shearing estimates of 21 crustal shortening for the region suggest that the crustal thickness prior to deformation was approximately 20 km in this part of the northern apennines

strain partitioning in ductile shear zones an example from a lower pennine nappe of switzerland abstract the rocks of the maggia nappe a lower pennine nappe of the swiss alps were deformed in at least three phases during alpine orogeny hercynian granites in the core of the nappe developed ductile shear zones during the early phases of deformation but between shear zones they remained almost undeformed both heterogeneous simple shear and heterogeneous volume change played an important role in the formation of the ductile shear zones partitioning of different strain components indicates a volume loss of nearly 80 90 towards the centres of some of the shear zones such a large amount of volume loss is also corroborated by strain analysis of deformed xenoliths in other shear zones of the same region a comparative study of theoretical strain paths and the natural results indicates constant shear strain rate but changing dilation rate during deformation

strain compatibility and shear zones is there a problem in analyzing deformation in rocks it is important to ensure that the solutions obtained satisfy strain compatibility this creates a challenge to understanding patterns of strain associated with shear zones in which measured strain may appear incompatible with the strain in the shear zone walls flattening strains are common in natural shear zones with locally straight and parallel boundaries to satisfy compatibility conditions such strains require volume loss across the shear zone or deviations from plane strain with or without discontinuities between the shear zone and the wall rock in the case of shear zones for which there is no evidence of volume loss or discontinuities along the shear zone walls problems of strain compatibility may be resolved if individual shear zones are linked together in an appropriate fashion shear zones commonly occur in anastomosing arrays and simple configurations of such arrays and the strains associated with them are examined it is shown that local transpression with strain compatibility can be accounted for in this way quite complex local strain patterns can develop in simple arrays

the solid body tilt of deformed paleohorizontal planes application to an archean transpression zone southern canadian shield abstract the solid body tilt sbt of deformed paleohorizontal planes is equal to the angle between their unstrained top direction and an upward pointing vertical axis kinematic models of important tectonic processes such as transpression and ductile thrusting have specific sbt requirements these models can be tested in ancient and modern orogens by determining the actual sbt of strata early magmatic sills and late horizontal intrusions with relict primary layering classical transpression models predict that except for sheath structures all folds in bedding be upright and horizontal i e that sbt values be close to zero within the hinge zones moreover all passive folding is accomplished by amplification of asperities and caused by the pure shear component of the transpression tensor nine sbt analyses were made in the archean crust of northwest ontario to test the transpression hypothesis north of the quetico wabigoon boundary western superior province central canada the nine sbt values do not discredit the hypothesis that the quetico fault marks an archean transpression zone which included the wabigoon rocks adjacent to the quetico metasediments

pressure solution deformation of the purgatory conglomerate rhode island u s a quantification of volume change real strains and sedimentary shape factor abstract pressure solution has caused substantial volume redistribution within the purgatory conglomerate from rhode island material has been removed from quartzite cobble surfaces parallel to the fold axes and mostly redeposited as fibrous pressure shadows at the long axis terminations of the cobbles in the hinges of folds 23 of the mean cobble volume has been removed and in highly deformed and overturned fold limbs up to 55 volume reduction has occurred the initial cobble shape and orientation can be measured at an undeformed locality and the deformation path can be easily deduced thus these are real cobble volume reductions apparent volume losses initial shapes not removed range from 70 to 89 real strains for cobbles axial ratios ranging from 1 0 65 0 38 to 1 0 47 0 15 have values of e x e y e z which range from 0 20 11 to 0 37 42 respectively depending on structural position the conglomerate itself has been extended parallel to the fold axes e r but the extension is not recorded by the cobble shapes

modeling the influence of tectonic extrusion and volume loss on the geometry displacement vorticity and strain compatibility of ductile shear zones oblate strains are often observed in meso scale ductile shear zones and this is generally taken to indicate narrowing across the shear zone during formation volume loss is one mechanism that could produce shear zone narrowing however not all shear zones display characteristics consistent with volume loss and in such cases the narrowing must be accomplished by the extrusion of material from within the shear zone to explore the relationship between shear zone geometry volume loss and extrusion shear zones were mathematically modeled results demonstrate the important influence of pure shear and volume loss on controlling the geometry displacement and vorticity of ductile shear zones further volume loss does not preclude extrusion unless for a given volume loss the strain is of a specific geometry extrusion is a likely mechanism important in shear zone development even if volume loss occurs extrusion presents strain compatibility problems because unlike crustal scale shear zones meso scale ductile shear zones do not possess a free surface if extrusion occurs bulk strain compatibility can be maintained if shear zones interlink in anastomosing arrays or change in thickness though not all shear zone systems display such characteristics modeling results elucidate the deformation style of shear zone in the northwest adirondacks in ny and in the kebnekaise region in northern sweden

the impact of groundwater drawdown and vacuum pressure on sinkhole development physical laboratory models abstract a considerable proportion of the damaging sinkholes worldwide correspond to human induced subsidence events related to groundwater withdrawal and the associated water table decline e g aquifer overexploitation dewatering for mining buoyancy loss in pre existing cavity roofs is generally claimed to be the main underlying physical mechanism it has been also postulated that rapid water table drawdowns may create a vacuum effect in the subsurface and contribute to enhance sinkhole activity in karstic terrains with a low effective porosity cover our laboratory physical model explores the role played by vacuum pressure induced water table drops with different magnitudes and rates on sinkhole development simulating an invariable mantled karst comprising cavernous bedrock and a low permeability cover the multiple tests performed include real time monitoring of the water level drawdown magnitude duration rate the negative air pressures in the bedrock cavity and the cover and several features of the subsidence phenomena deformation style size magnitude rate the main findings derived from the test results include 1 vacuum pressure may trigger the development of cover collapse sinkholes in areas with low permeability covers 2 different water table decline patterns magnitude duration rate may result in different subsidence styles or rheological behaviours sagging versus collapse 3 ground fissuring frequently related to extension at the margin of sagging depressions may cancel or significantly diminish the vacuum effect 4 an overall direct relationship between the water table decline rate and the subsidence rate some possible strategies are proposed to ameliorate the adverse effect of the negative air pressure on sinkhole hazard which most probably has a local impact restricted by the concurrence of rapid water drawdowns and low permeability covers

strain in ductile shear zones in the caledonides of northern sweden a three dimensional puzzle small scale ductile shear zones are well developed in amphibolites of caledonian nappes of the swedish lapland strain in the shear zones is recorded by the shapes of originally sub equant aggregates of plagioclase feldspar classical strain analysis on two dimensional xz profiles across the shear zones leads to results that indicate large volume losses associated with the shear strain large volume losses are however incompatible with geochemical analysis which shows little chemical variation across the shear zones by including data from xy and yz sections information on the three dimensional state of strain can be obtained these data indicate that deformation is not confined to a two dimensional plane particle extension within the shear zone parallel to the shear plane and perpendicular to the shear direction has also occurred the state of strain and strain path in the shear zone can be modeled in a general way by combining stretches in x y and z with simple shearing and volume loss end member models correspond to plane strain with volume loss kx ky 1 kz 1 transpression kx 1 ky 1 kz and pure shear kx 1 kz ky 1 these models produce identical strain ratios and orientations on the xz section but differ in stretch in y and in area of the strain ellipse on the xz section extension in y or x allows for reconciliation of the geometrical and geochemical data for part of an individual shear zone but poses a problem of strain compatibility at the edges and terminations of the shear zones the shear zones show a complex anastomosing pattern in three dimensions and their connectivity provides a way in which strain compatibility is maintained

application of limit plasticity to the stability of sinkholes abstract a solution is obtained using classical plasticity theory and the method of characteristics to evaluate the stability of soils adjacent to a cylindrical void the soil strength contains both cohesive and frictional components which allows the solution to be used to evaluate the drained stability of residual soils overlying cavitose bedrock the method yields a lower bound solution for the magnitude of a surface loading required to cause instability of the system and provides a description of the slip line defining the failure zone the results are compared in dimensionless terms for various combinations of cavity diameter and overburden thickness for a given overburden thickness small cavities are more stable than large cavities however for a given cavity diameter large overburden thicknesses are shown to be more stable than small thicknesses this is contrary to conventional slope stability where stability generally decreases with increasing height the difference is attributed to the role of a circumferential stress component in the axisymmetric solution which may be significant for small diameter cavities equations are suggested for the determinaton of the vertical stress required to generate an instability and for estimation of the size or surface extent of damage these results have significance in soil stability analyses in karst terrain and in the construction of deep foundations such as drilled shafts the improvement of methods to detect and measure voids in soil fischer and canace 1989 will make this method particularly attractive

structure of hood lake syenite an undeformed archean pluton in the western superior province southern canadian shield abstract the hood lake syenite is a late archean pluton that has escaped significant tectonic deformation the intrusive contact dips inward in most localities which provides some constraint of its three dimensional geometry the pluton has a concordant planar fabric of perthite megacrysts and could have grown by mature diapirism mushrooming as well as by in situ ballooning only magmatic diapirism seems to be capable of explaining the heart like map pattern of the pluton and its location at the junction of two vertical zones of weakness a regional fault and a ductile shear zone

strain and possible volume loss in a high grade ductile shear zone small scale ductile shear zones in high grade metagabbros from the caledonides of northern sweden provide a good opportunity for examining the development of fabric and strain in rocks undergoing progressive non coaxial deformation the rocks contain strain markers in the form of aggregates of plagioclase feldspar a selected shear zone is analyzed assuming monoclinic symmetry which requires for the zone as a whole variable simple shear variable volume change or variable simple shear and volume change plus a homogeneous deformation both size of the feldspar aggregates and aspect ratio of the aggregates plotted against orientation indicate significant volume decrease in excess of 50 and perhaps as much as 80 towards the centers of the zones the data are broadly consistent with a deformation path involving constant shear strain across the zone followed by variable volume change or by a path of progressive loss of volume with increasing shear strain followed by a homogeneous strain they are not consistent with a single path involving rates of shear strain and volume loss that are in constant proportions there is little difference in chemical composition between the shear zone and the surrounding rock an analysis of the concentrations of elements in the shear zone and wall rock suggests that volume changes were slight 15 the discrepancy between the values of volume change estimated from strain analysis and geochemical analysis may be resolved either by geochemical equilibration being attained after deformation or by a departure from the geometric constraints of the monoclinic band model for shear zones modification of marker particle size and shape during dynamic recrystallization may also partly account for the apparent volume loss