Pseudo 3-D modeling of trishear fault-propagation folding

Basement structures, to which trishear fault-propagation models have most successfully been applied, are commonly three-dimensional folds formed at the tip-line of a fault. We present here a ‘pseudo-3D’ trishear model in which various parameters are permitted to vary along strike and oblique-slip can be modeled. These variations may be combined in an infinite number of ways, facilitating the simulation of many real structures. A thrust changing from blind to emergent can be produced by a change in the slip or propagation-to-slip (P/S) along strike. Folds with forelimbs changing from overturned to upright along strike can be modeled either by changing the slip, P/S or trishear angle. Also some minor folds perpendicular or oblique to the main structure can result from changes in the trishear angle or fault angle along the strike. Models including growth strata show that it is practically impossible to distinguish between growth and pre-growth strata using the map patterns. As a field test, we have modeled the oblique slip East Kaibab monocline, demonstrating a good fit between the field observations and model predictions.     

Lithospheric scale folding: numerical modelling and application to the Himalayan syntaxes

 We describe the eastern and western Himalayan syntaxes, which are large-scale antiforms situated at geodynamically similar locations and the metamorphic evolution of which is coeval in the India–Asia collisional history. To understand the mechanical plausibility of the structural interpretation, we present two-dimensional finite-element modelling of lithospheric folding. The models reveal the coeval development of adjacent synformal basins, analogous to the Peshawar and Kashmir basins on both sides of the western syntaxis. Similarities between geological data and calculated models indicate that lithospheric buckling is a basic response to large-scale continental shortening and an efficient mountain building process. Received: 26 November 1998 / Accepted: 27 November 1998     

Discrete element modelling of fragmentable geomaterials with size dependent strength

This paper presents the application of a discrete element technique to the analysis of the dynamic indentation of either a purely brittle or a brittle viscoplastic geomaterial which can experience fragmentation resulting in fragments with size dependent strength characteristics.     

The impact of cover rock rheology on the style of folding in the Zagros fold-thrust belt

The present day morphology of the Zagros fold-thrust belt is dominated by magnificent exposures of NW–SE trending folds. These folds differ in their size and geometry and these differences are related mainly to the rheological profile of the cover rock. The cover rock succession of the Zagros consists of a sequence of competent and incompetent units which vary both along and across the belt. Field based study combined with the use of satellite images reveals that the thickness and facies distribution of the cover rock succession has a significant impact on the style of deformation. During the shortening linked to the current convergence of the Arabian and Iranian plates, the incompetent units act as detachment horizons which localise thrusting and which act as décollement above which detachment folds form. In addition, where these incompetent units are thick (e.g.> 1 km), they allow the deformation above and below them to become completely decoupled enabling disharmonic folding to occur. As a result the folds above and below the incompetent units in the central part of the Zagros Folded Belt, have significantly different geometries and wavelengths. As the Zagros folds host the majority of the hydrocarbon reserves in Iran and Iraq, an understanding of the processes that influence their geometry and spatial organization at different levels in the cover rock is crucial for the future exploration in the region.     

Separation of rifting and lithospheric folding signatures in the NW-Alpine foreland

The development of the Alpine mountain belt has been governed by the convergence of the African and European plates since the Late Cretaceous. During the Cenozoic, this orogeny was accompanied with two major kinds of intraplate deformation in the NW-European foreland: (1) the European Cenozoic Rift System (ECRIS), a left-lateral transtensional wrench zone striking NNE-SSW between the western Mediterranean Sea and the Bohemian Massif; (2) long-wavelength lithospheric folds striking NE and located between the Alpine front and the North Sea. The present-day geometry of the European crust comprises the signatures of these two events superimposed on all preceding ones. In order to better define the processes and causes of each event, we identify and separate their respective geometrical signatures on depth maps of the pre-Mesozoic basement and of the Moho. We derive the respective timing of rifting and folding from sedimentary accumulation curves computed for selected locations of the Upper Rhine Graben. From this geometrical and chronological separation, we infer that the ECRIS developed mostly from 37 to 17 Ma, in response to north-directed impingement of Adria into the European plate. Lithospheric folds developed between 17 and 0 Ma, after the azimuth of relative displacement between Adria and Europe turned counter-clockwise to NW–SE. The geometry of these folds (wavelength = 270 km; amplitude = 1,500 m) is consistent with the geometry, as predicted by analogue and numerical models, of buckle folds produced by horizontal shortening of the whole lithosphere. The development of the folds resulted in ca. 1,000 m of rock uplift along the hinge lines of the anticlines (Burgundy–Swabian Jura and Normandy–Vogelsberg) and ca. 500 m of rock subsidence along the hinge line of the intervening syncline (Sologne–Franconian Basin). The grabens of the ECRIS were tilted by the development of the folds, and their rift-related sedimentary infill was reduced on anticlines, while sedimentary accumulation was enhanced in synclines. We interpret the occurrence of Miocene volcanic activity and of topographic highs, and the basement and Moho configurations in the Vosges–Black Forest area and in the Rhenish Massif as interference patterns between linear lithospheric anticlines and linear grabens, rather than as signatures of asthenospheric plumes.

Discrete element modelling of creep of asphalt mixtures

Creep tests on asphalt mixtures have been undertaken under four stress levels in the laboratory while the discrete element model (DEM) has been used to simulate the laboratory tests. A modified Burger’s model has been used to represent the time-dependent behaviour of an asphalt mixture by adding time-dependent moment and torsional resistance at contacts. Parameters were chosen to give the correct stress-strain response for constant strain rate tests in Cai et al. (2013). The stress-strain response for the laboratory creep tests and the simulations were recorded. The DEM results show reasonable agreement with the experiments. The creep simulation results proved to be dependent on both bond strength variability and positions of the particles. Bond breakage was recorded during the simulations and used to investigate the micro-mechanical deformation behaviour of the asphalt mixtures. An approach based on dimensional analysis is also presented in this paper to reduce the computational time during the creep simulation, and this analysis is also a new contribution.     

Discrete element modelling of cyclic behaviour of granular materials

Discrete Element Modeling (DEM) of cyclic behavior of granular material has been attempted to understand liquefaction behavior of sands. A series of cyclic biaxial tests in both undrained and drained conditions with constant stress and strain amplitudes were performed on assemblage of loose and dense systems. Tests are conducted on monodisperse (uniform) and polydisperse (well graded) samples. From this study, it has been shown that DEM can simulate the cyclic behavior of sands very satisfactorily. Characteristic features, i.e., occurrence of large plastic strains and changing over from contractile to dilative behavior beyond the phase transformation angle, anisotropy of reduced strength on the extension side etc are very well reflected in numerical simulations. Liquefaction of loose assemblage seems to be mainly due to continued and cumulative loss of co-ordination number under each cycle as there is a reversal of loading direction and hence a continuous reorientation of fabric. There is no cumulative loss of co-ordination number in dense states because the stress ratios are mostly higher than the phase transformation level where the fabric has reached a limiting orientation. Micro mechanical explanations to the macroscopic behavior of the disc assemblage under cyclic loading are presented in terms of the force and fabric anisotropy coefficients.     

Discrete element modelling of deep penetration in granular soils

This paper presents a numerical study on deep penetration mechanisms in granular materials with the focus on the effect of soil–penetrometer interface friction. A two‐dimensional discrete element method has been used to carry out simulation of deep penetration tests on a granular ground that is under an amplified gravity with a K₀ lateral stress boundary. The numerical results show that the deep penetration makes the soil near the penetrometer move in a complex displacement path, undergo an evident loading and unloading process, and a rotation of principal stresses as large as 180°. In addition, the penetration leads to significant changes in displacement and velocity fields as well as the magnitude and direction of stresses. In general, during the whole penetration process, the granular ground undergoes several kinds of failure mechanisms in sequence, and the soil of large deformation may reach a stress state slightly over the strength envelope obtained from conventional compression tests. Soil–penetrometer interface friction has clear effects on the actual penetration mechanisms. Copyright © 2005 John Wiley & Sons, Ltd.     

Late Pleistocene and Holocene paleoseismology of an intraplate seismic zone in a large alluvial valley, the New Madrid seismic zone, Central USA

The New Madrid seismic zone (NMSZ) is an intraplate right-lateral strike-slip and thrust fault system contained mostly within the Mississippi Alluvial Valley. The most recent earthquake sequence in the zone occurred in 1811–1812 and had estimated moment magnitudes of 7–8 (e.g., [Johnston, A.C., 1996. Seismic moment assessment of stable continental earthquakes, Part 3: 1811–1812 New Madrid, 1886 Charleston, and 1755 Lisbon. Geophysical Journal International 126, 314–344; Johnston, A.C., Schweig III, E.S, 1996. The enigma of the New Madrid earthquakes of 1811–1812. Annual Reviews of Earth and Planetary Sciences 24, 339–384; Hough, S.E., Armbruster, J.G., Seeber, L., Hough, J.F., 2000. On the modified Mercalli intensities and magnitudes of the New Madrid earthquakes. Journal of Geophysical Research 105 (B10), 23,839–23,864; Tuttle, M.P., 2001. The use of liquefaction features in paleoseismology: Lessons learned in the New Madrid seismic zone, central United States. Journal of Seismology 5, 361–380]). Four earlier prehistoric earthquakes or earthquake sequences have been dated A.D. 1450 ± 150, 900 ± 100, 300 ± 200, and 2350 B.C. ± 200 years using paleoliquefaction features, particularly those associated with native American artifacts, and in some cases surface deformation ([Craven, J. A. 1995. Paleoseismology study in the New Madrid seismic zone using geological and archeological features to constrain ages of liquefaction deposits. M.S thesis, University of Memphis, Memphis, TN, U.S.A.; Tuttle, M.P., Lafferty III, R.H., Guccione, M.J., Schweig III, E.S., Lopinot, N., Cande, R., Dyer-Williams, K., Haynes, M., 1996. Use of archaeology to date liquefaction features and seismic events in the New Madrid seismic zone, central United States. Geoarchaeology 11, 451–480; Guccione, M.J., Mueller, K., Champion, J., Shepherd, S., Odhiambo, B., 2002b. Stream response to repeated co-seismic folding, Tiptonville dome, western Tennessee. Geomorphology 43(2002), 313–349; Tuttle, M.P., Schweig, E.S., Sims, J.D., Lafferty, R.H., Wolf, L.W., Haynes, M.L., 2002. The earthquake potential of the New Madrid seismic zone, Bulletin of the Seismological Society of America, v 92, n. 6, p. 2080–2089; Tuttle, M.P., Schweig III, E.S., Campbell, J., Thomas, P.M., Sims, J.D., Lafferty III, R.H., 2005. Evidence for New Madrid earthquakes in A.D. 300 and 2350 B.C. Seismological Research Letters 76, 489–501]). The two most recent prehistoric and the 2350 B.C. events were probably also earthquake sequences with approximately the same magnitude as the historic sequence.Surface deformation (faulting and folding) in an alluvial setting provides many examples of stream response to gradient changes that can also be used to date past earthquake events. Stream responses include changes in channel morphology, deviations in the channel path from the regional gradient, changes in the direction of flow, anomalous longitudinal profiles, and aggradation or incision of the channel ([Merritts, D., Hesterberg, T, 1994. Stream networks and long-term surface uplift in the New Madrid seismic zone. Science 265, 1081–1084.; Guccione, M.J., Mueller, K., Champion, J., Shepherd, S., Odhiambo, B., 2002b. Stream response to repeated co-seismic folding, Tiptonville dome, western Tennessee. Geomorphology 43 (2002), 313–349]). Uplift or depression of the floodplain affects the frequency of flooding and thus the thickness and style of vertical accretion or drowning of a meander scar to form a lake. Vegetation may experience trauma, mortality, and in some cases growth enhancement due to ground failure during the earthquake and hydrologic changes after the earthquake ([VanArdale, R.B., Stahle, D.W., Cleaveland, M.K., Guccione, M.J., 1998. Earthquake signals in tree-ring data from the New Madrid seismic zone and implications for paleoseismicity. Geology 26, 515–518]). Identification and dating these physical and biologic responses allows source areas to be identified and seismic events to be dated.Seven fault segments are recognized by microseismicity and geomorphology. Surface faulting has been recognized at three of these segments, Reelfoot fault, New Madrid North fault, and Bootheel fault. The Reelfoot fault is a compressive stepover along the strike-slip fault and has up to 11 m of surface relief ([Carlson, S.D., 2000. Formation and geomorphic history of Reelfoot Lake: insight into the New Madrid seismic zone. M.S. Thesis, University of Arkansas, Fayetteville, Arkansas, U.S.A]) deforming abandoned and active Mississippi River channels ([Guccione, M.J., Mueller, K., Champion, J., Shepherd, S., Odhiambo, B., 2002b. Stream response to repeated co-seismic folding, Tiptonville dome, western Tennessee. Geomorphology 43 (2002), 313–349]). The New Madrid North fault apparently has only strike-slip motion and is recognized by modern microseismicity, geomorphic anomalies, and sand cataclasis ([Baldwin, J.N., Barron A.D., Kelson, K.I., Harris, J.B., Cashman, S., 2002. Preliminary paleoseismic and geophysical investigation of the North Farrenburg lineament: primary tectonic deformation associated with the New Madrid North Fault?. Seismological Research Letters 73, 393–413]). The Bootheel fault, which is not identified by the modern microseismicity, is associated with extensive liquefaction and offset channels ([Guccione, M.J., Marple, R., Autin, W.J., 2005, Evidence for Holocene displacements on the Bootheel fault (lineament) in southeastern Missouri: Seismotectonic implications for the New Madrid region. Geological Society of America Bulletin 117, 319–333]). The fault has dominantly strike-slip motion but also has a vertical component of slip. Other recognized surface deformation includes relatively low-relief folding at Big Lake/Manila high ([Guccione, M.J., VanArdale, R.B., Hehr, L.H., 2000. Origin and age of the Manila high and associated Big Lake “Sunklands”, New Madrid seismic zone, northeastern Arkansas. Geological Society of America Bulletin 112, 579–590]) and Lake St. Francis/Marked Tree high ([Guccione, M.J., VanArsdale, R.B., 1995. Origin and age of the St. Francis Sunklands using drainage patterns and sedimentology. Final report submitted to the U. S. Geological Survey, Award Number 1434-93-G-2354, Washington D.C.]), both along the subsurface Blytheville arch. Deformation at each of the fault segments does not occur during each earthquake event, indicating that earthquake sources have varied throughout the Holocene.     

Discrete element modeling of the faulting in the sedimentary cover above an active salt diapir

Geological mapping, seismic analyses, and analogue experiments show that active salt diapirism results in significant faulting in the overburden strata. Faults associated with active diapirism generally develop over the crest of the dome and form a radial pattern. In this study, we have created a 3-D discrete element model and used this model to investigate the fault system over active diapirs. The model reproduces some common features observed in physical experiments and natural examples. The discrete element results show that most faults initiate near the model surface and have displacement decreasing downward. In addition, model results indicate that the earliest fault, working as the master fault, has a strong influence on the subsequent fault pattern. The footwall of the master fault is mainly deformed by arc-parallel stretching and develops a subradial fault pattern, whereas the hanging wall is deformed by both arc-parallel stretching and gliding along the master fault and top of salt, and hence develops both parallel and oblique faults. Model results replicate the fault pattern and deformation mechanism of the Reitbrook dome, Germany.     

堆石料颗粒形状对堆积密度及强度影响的离散元分析

颗粒形状不仅反映颗粒的形成历史,更是影响堆石料物理力学性能的重要因素之一,值得深入研究。采用颗粒流程序PFC3D,根据实际颗粒形状建立不同球度的颗粒模型,并提出了数值试验中获取不同相对密实度试样的流程。讨论了球度对最大、最小孔隙比的影响,其结论与已有试验统计结果基本相符。分别以孔隙比和相对密实度为密度控制指标,对不同颗粒形状的试样进行等向固结和常规三轴试验,并分析了配位数、颗粒长轴各向异性、接触各向异性、结构各向异性等微观变量的变化规律。结果表明,当颗粒圆度较高且级配均匀时,球度对峰值摩擦角影响较小,主要影响残余摩擦角的大小。颗粒形状发生变化时,配位数影响试样强度但不起决定性作用,颗粒形状主要通过影响试样内接触以及接触力的各向异性程度来影响试样宏观表现。     

Discrete element modelling of rock cutting: from ductile to brittle transition

It is well accepted that there is a transition of failure mode from ductile to brittle with increasing depth of cut during rock cutting process. Rock failure modes affect cutting efficiency, and knowledge of the failure transition is essential to the determination of optimum cutting parameters. The critical transition depth can be linked with rock properties. In this study, an attempt was made to model rock cutting process and to check the dependence of the critical failure mode transition depth on the brittleness of rock. For this purpose, dimensional analysis was first performed to establish the correlations between rock macro‐properties and micro‐parameters for discrete element simulations. Following the specimen calibration procedure, two types of synthetic rocks having approximately the same uniaxial compressive strength were generated as the synthetic specimens for simulating the rock cutting process. The first specimen was created using conventional model construction method with identical bond strengths between particles, giving rise to undesirably high indirect tensile strength. The second specimen was created using a proposed clustering algorithm such that the ratio between the tensile and compressive strength matches reasonably well with that of real rocks. The results of rock cutting simulations demonstrate that failure mode transition took place in both models, but for the clustered model the transition emerged at a shallower cutting depth. A further exploration was made to derive the critical depth for this transition based on the simulations performed on the clustered models. The derived relationship indicates that the critical transition depth decreases as strength ratio or brittleness of the rock increases. This provides a very useful tool for predicting the critical depth which can be used to help cutting tool design and cutting parameter optimisations. Copyright © 2015 John Wiley & Sons, Ltd.     

Discrete element modelling of an underground explosion in a jointed rock mass

The purpose of this paper is to investigate the application of the discrete element program UDEC for modelling underground explosions in a jointed rock mass. A field underground explosion test has been conducted and UDEC and AUTODYN were utilised in a coupled manner to predict the rock mass response due to the underground explosion. The dynamic equation for the state of the rock material obtained from impact tests was incorporated into the calibration modelling. The comparison of modelling results with test results and empirical formulas shows that UDEC is capable of modelling explosion wave propagation in jointed rock mass with high reliability.     

各向异性对软土力学特性影响的离散元模拟

软土预压工程中,初始和诱发各向异性对软土力学性质的影响十分显著,而现有研究缺乏对初始和诱发各向异性的统一研究方法。采用离散单元法,以颗粒长宽比作为定量评价指标,构建真实形态的颗粒模型,生成5组不同沉积角的初始各向异性试样,并进行竖直和水平两方向加载的双轴模拟实验,研究了初始各向异性和诱发各向异性对软土力学特性影响;在细观层面,以颗粒为对象研究了颗粒接触形式和转动角度的变化规律,以接触为对象研究了配位数和接触法向各向异性的发展趋势,在此基础上探究抗剪强度指标与各向异性关系。结果表明：初始和诱发各向异性共同影响试样力学性质,当加载方向和软土沉积方向垂直时,土体有最大的峰值强度。颗粒接触形式中面面接触的比例随加载的进行逐渐增大,并影响着试样初始模量和抗剪强度,配位数和接触法向各向异性受颗粒接触形式的影响有不同的演化规律,并在加载后期趋于稳定;同时,初始各向异性试样相较各向同性试样有更大的黏聚力,诱发各向异性主要影响试样内摩擦角,进而影响试样抗剪强度。     

贵州纳雍普洒滑坡动力触发机制离散元模拟分析

采用UDEC离散单元法数值模拟,再现了贵州纳雍张家湾镇普洒滑坡在煤层采空区、深大岩溶裂隙、强降雨和回采爆破振动协同作用下的动力响应特征,揭示出该崩滑的动力触发机制与主控因素。结果表明：（1）在原始坡体下伏煤层自下而上依次开采时,其采空区上覆岩层中“冒落带”、“裂缝带”和“弯曲下沉带”范围逐渐扩大,当位于最上部的煤层被开采后,其上覆岩层中发育的“弯曲下沉带”已触及坡脚;期间该原始坡体处于累积变形阶段,其变形具有明显的整体“下座”和“顺时针旋转”特征;（2）在强降雨作用时,已受采空区作用的坡体进入累积变形扩大阶段,其宏观变形仍具有“下座”和“顺时针旋转”特征;（3）当回采爆破振动持续作用时,已受采空区和强降雨耦合作用的变形坡体进入持续“渐进损伤”、“临界崩滑”、“解体破碎”、“震荡抛射”和“堆积压实”动力响应阶段,期间滑坡体宏观位移表现出明显的“下座”、“溃屈”和“顺时针旋转”特征。     

Discrete element modelling of material non‐coaxiality in simple shear flows

We investigate the quasi‐static simple shear flow of a two‐dimensional assembly of cohesionless particles using discrete element method (DEM) simulations. We focus on the unsteady flow regime where the solid would experience significant evolution of stresses, mobilised shear strength and dilation. We construct the DEM model using a discretised‐wall confined granular cell where the apparent boundary is allowed to dilate or contract synchronously with the confined solid. A rather uniform simple shear field is achieved across the whole assembly, which benefits rheological studies in generalising constitutive laws for continuum methods. We examine two aspects of the simple shear behaviour: macroscopic stress and strain rate evolution, particularly the non‐coaxiality between the principal directions of the two; and micromechanics such as evolution of fabric. For an initially anisotropic specimen sheared under constant normal pressure, the direction of principal stress rotates towards that of the principal strain rate, gradually reducing the degree of non‐coaxiality from about 45° to fluctuating around 0°. The rate in approaching coaxiality is slower in samples with larger initial porosity, stress ratio and mean stress. Generally, a faster rate in approaching coaxiality in simple shear is observed in a more dilatant sample, which often shows a larger degree of mobilised fabric anisotropy, suggesting the possible important role of instantaneous internal friction angle. The evolution of principal fabric direction resembles that of the principal stress direction. © 2013 The Authors. International Journal for Numerical and Analytical Methods in Geomechanics published by John Wiley & Sons, Ltd.     

An approach to folding kinematics from the analysis of folded oblique surfaces

Two-dimensional analysis of folded surfaces oblique to the mechanical layering can shed light on the kinematic mechanisms that operated during the development of folds. A new version of the program ‘FoldModeler’, developed in the Mathematica™ environment, is used to obtain the deformed configuration of an initial pattern of oblique surfaces deformed by any combination of the most common kinematic folding mechanisms: flexural flow, tangential longitudinal strain, with or without area change and heterogeneous simple shear. The layer can also undergo any form of homogeneous strain at any moment of the folding process. The outputs of the program provide complete information about the strain distribution in the folded layer that includes graphs of the angle between the oblique surfaces as a function of the inclination of the layering through the fold. These graphs can be very useful to discriminate between the mechanisms that operate in the development of natural folds, and they have been obtained and discussed for the most common combinations of strain patterns. The program is applied to obtain theoretical folds that give a good fit of some natural examples of folded oblique surfaces.     

Coeval folding and boudinage under plane strain with the axis of no change perpendicular to the layer

Plane-strain coaxial deformation of a competent plasticine layer embedded in an incompetent plasticine matrix was carried out to improve our understanding about the evolution of folds and boudins if the layer is oriented perpendicular to the Y-axis of the finite strain ellipsoid. The rock analogues used were Beck’s green plasticine (matrix) and Beck’s black plasticine (competent layer), both of which are strain-rate softening modelling materials with a stress exponent n=ca. 8. The effective viscosity η of the matrix plasticine was changed by adding different amounts of oil to the original plasticine. At a strain rate of 10⁻³ s⁻¹ and a finite strain e of 10%, the effective viscosity of the matrix ranges from 1.2×10⁶ to 7.2×10⁶ Pa s. The effective viscosity of the competent layer has been determined as 4.2×10⁷ Pa s. If the viscosity ratio is large (ca. 20) and the initial thickness of the competent layer is small, both folds and boudins develop simultaneously. Although the growth rate of the folds seems to be higher than the growth rate of the boudins, the wavelength of both structures is approximately the same as is suggested by analytical solutions. A further unexpected, but characteristic, aspect of the deformed competent layer is a significant increase in thickness, which can be used to distinguish plane-strain folds and boudins from constrictional folds and boudins.An erratum to this article can be found at     

Discrete element analysis of the influence of bolt pattern and spacing on the force-displacement response of bolted steel mesh

Steel wire mesh held by a pattern of bolts can be used to stabilize a rock slope. Knowledge of the force-displacement response of steel mesh is essential in the design of this support system. Laboratory tests have been used to test mesh that is held to rigid steel frames. These testing conditions differ from how steel mesh is held in the field by bolts. The existing laboratory test data may underestimate the deformation and overestimate the load-bearing capacity of the steel mesh. This paper focuses on the response of the high tensile strength steel mesh held by commonly used bolt patterns. Discrete element models were used to study the force-displacement response of the steel mesh pinned by bolts. The influences of different bolt patterns and varying ratios of bolt spacing on the effectiveness of steel wire mesh were analyzed. Relationships between the resistance force of steel mesh and bolt density at various mesh deformations were developed. These relationships can help engineers choose the bolt spacing and provide an estimate of the resistance force that a steel mesh can mobilize at a desired deformation limit for a given bolt pattern.     

A range of fault slip styles on progressively misoriented planes during flexural-slip folding,Cape Fold Belt,South Africa

Flexural slip folds are distinctive of mixed continuous-discontinuous deformation in the upper crust, as folding is accommodated by continuous bending of layers and localized, discontinuous slip along layer interfaces. The mechanism of localized, layer-parallel slip and the stress and fluid pressure conditions at which flexural slip occurs are therefore distinctive of shear localization during distributed deformation. In the Prince Albert Formation mudstone sequence of the Karoo Basin, the foreland basin to the Cape Fold Belt, folds are well developed and associated with incrementally developed bedding-parallel quartz veins with slickenfibers oriented perpendicular to fold hinge lines, locally cross-cutting axial planar cleavage, and showing hanging wall motion toward the fold hinge. Bedding-parallel slickenfiber-coated veins dip at angles from 18° to 83°, implying that late increments of bedding-parallel shear occurred along unfavorably oriented planes. The local presence of tensile veins, in mutually cross-cutting relationship with bedding-parallel, slickenfiber-coated veins, indicate local fluid pressures in excess of the least compressive stress.Slickenfiber vein microstructures include a range of quartz morphologies, dominantly blocky to elongate-blocky, but in places euhedral to subhedral; the veins are commonly laminated, with layers of quartz separated by bedding-parallel slip surfaces characterized by a quartz-phyllosilicate cataclasite. Crack-seal bands imply incremental slickenfiber growth, in increments from tens of micrometers to a few millimeters, in some places, whereas other vein layers lack evidence for incremental growth and likely formed in single slip events. Single slip events, however, also involved quartz growth into open space, and are inferred to have formed by stick-slip faulting. Overall, therefore, flexural slip in this location involved bedding-parallel faulting, along progressively misoriented weak planes, with a range of slip increments.