Jean-Pierre Petit

Joint spacing: analogue and numerical simulations

Abstract Joint spacing distribution laws remain a controversial subject in the literature. In order to understand joint spacing, analogue and numerical modelling techniques were used. In the analogue model an evolution of the joint spacing distribution law during fracture development was observed as new fractures appear. Different processes for fracture initiation and propagation have been tested numerically including mid-point fracturing and partially or completely random processes. This study suggests that an initiation of fractures according to a random process could explain real joint spacing distributions. An evolution of joint spacing distribution laws from initially negative exponential to log-normal and normal is found with increasing joint development.

Palaeostress superimposition deduced from mesoscale structures in limestone: the Matelles exposure, Languedoc, France

Abstract This study investigates the reasons for the superimposition of several maximum principal stress directions (σ1) in the same area, and examines the contrast between unperturbed areas (stable direction of σ1) and perturbed areas (changing σ1 direction). We studied mesoscale structures on a 1000 m2 continuous limestone exposure near a regional scale strike-slip fault. Local σ1 directions were deduced from a high concentration of minor strike-slip faults, extension fractures and stylolites formed during the Pyrenean shortening in Languedoc, France. Most of the stylolites were formed in a stress field which was homogeneous on the exposure scale. This was followed by the reactivation of pre-existing extension fractures as strike-slip faults whose activity determined stress perturbations. A very heterogeneous stress field was produced leading to the formation of new localized stylolites and extension fractures, especially at fault terminations and at oversteps. Thus the final pattern shows the superimposition of all these structures. Reactivation of structures was caused by slight temporal changes in the orientation and intensity of the stress field produced by the nearby regional strike-slip faults. Our study suggests that the origin of stress deviations or superimpositions cannot be explained by random measurements of σ1. It is essential to be able to synthesize the fault pattern and the stress trajectories which it determines, and to do this, a very high density or a selection of data from mesoscale structures is needed.

Analogue simulation of natural orthogonal joint set formation in brittle varnish

Abstract Two orthogonal joint sets are commonly observed in exposed sedimentary rocks with a wide variety of abutting and cross-cutting relationships. Brittle varnish analogue models are carried out in conjunction with field studies, in order to classify the different orthogonal fracture patterns and constrain the mechanical basis of orthogonal joint development. The results suggest that the stress which creates the second joint set can result from: (i) relaxation effects; (ii) slight tension due to warping of the bands defined by the first parallel fractures; and (iii) local and/or regional reversals between σ 2 and σ 3 . A ‘ladder’ pattern, formed by the combination of an initial set of long parallel joints and associated non-cross-cutting joints of the second set, is obtained if the shear strength of the initial joints is low during the development of the second set. A ‘grid’ pattern, where both sets mutually cross-cut, occurs when the shear strength of the initial joint set is high, possibly the result of a high normal stress or healing and could result from two independent stress events. An intermediate pattern comprising cross-cutting and abutting orthogonal cross-joints can form if the shear strength of the initial joints was intermediate and/or variable during the development of the second set. Mutually abutting joint sets are observed within each pattern and could result from stress reversals or low differential stress during the final stages of joint development. The classical presentation of joint data using rose diagrams cannot distinguish between the wide variety of orthogonal joint patterns. Maps of fracture intersections should compliment the orientation data. We discuss methods to estimate the joint pattern where intersection data are absent.

Joints in the Mesozoic sediments around the Bristol Channel Basin

Abstract Analysis has been carried out at four locations on the edges of the Bristol Channel Basin to illustrate the later phases of deformation of a sedimentary basin, and to illustrate the control on joint patterns of subtle changes in the stress system. The characteristics of the joints are described and influences on joints are determined, including the roles of faults, folds and beds. There is a low coefficient of correlation between joint spacing and bed thickness, except in very thin limestone beds, which have a high density of joints. The lengths and spacings of earlier joint phases are usually greater than those of later phases. Later joints normally abut against earlier joints. The joints abut the latest faults but are not displaced by them, so the joints post-date the main Alpine contraction. The joints formed in five main phases during reduction of the Alpine stresses. Phase 1 joints are sub-parallel to the regional compression direction (160–180°). Phase 2 joints are perturbed by faults, often curving towards points of stress concentrations along the faults. Phase 3 joints are sub-parallel to the earlier E–W-striking fold axes. Phase 4 joints are cross-joints, and phase 5 joints form polygonal patterns within joint-bound blocks. Phases 2 and 3 do not occur in the absence of faults and folds, and correspond with a reduction in horizontal compression and an increase in the importance of local factors. Phases 4 and 5 occur at all locations.

Cutting of the European continental lithosphere: Plasticity theory applied to the present Alpine collision

Presently active European Alpine collision has a history of more than 100 Myr convergence. We investigate the collisional contact problem of an apparently rigid African promontory (currently the Italy/Adria block (IAB)) steadily penetrating at 1 cm/yr, over at least the past 45 Myr, into the deformable European plate. We assume that neither continental subduction nor delamination occurs presently in the 300-km-wide contact zone enabling use of the indenter-indentee approach. A key parameter is the aspect ratio h/a, defined by the width of the deformable foreland over the width of the indenter itself. This parameter controls the activation of two fundamentally different modes of deformation: (1) classical indentation mode for h/a≥4.4, described by previous authors, and having effect only in a portion of the deformable plate in the vicinity of the indenter and (2) cutting mode for h/a<4.4 giving plane strain longitudinal splitting of the entire deformable plate and plastic separation of the two halves. We use a matrix operator method to solve for slip lines in the mixed boundary value problem (obliquity, velocity, friction, stress) of the European Alpine case. Implications are as follows: (1) plane stress, vertical lithospheric thickening is the first indentation mode of continental collision; and (2) for the present ratio of h/a≈3 deformation is in the cutting mode and slow plane strain intraplate extension (rifting) is predicted. This mode explains the intraplate stress field obtained from borehole and earthquake data. Considering that the paleoindenter probably has been larger than the IAB it is inferred that h/a has been below 4.4 since at least the end of the Eocene and that consequently the intraplate graben system (Lower Rhine, Rhine, Bresse, Limagne) is due to the cutting of the European plate by Alpine collision.

Micromechanics of shear rupture and the control of normal stress

Abstract Conjugate microfault zones and distributed tensile microcracks were observed in low porosity sandstone samples deformed by shear box rupture at different normal stresses. Statistical data collected from scanning electron microscopic mapping show that tensile microcracks and microfaults are more frequent in the higher normal stress cases. The average thickness of the cataclastic microfault zones increases proportionally to rupture normal stress. The density of tensile microcracks increases locally in microfault relay and intersection zones where their formation is an important mode of microfault zone cataclasis. Concentration of longer en echelon tensile microcracks occurs in process zones ahead of the microfault tips, connected by cross-cracks in an incipient breakdown zone to further propagate the fault. Fracture densities are much lower in calcite cement grains whose compliancy serves to arrest microfault growth temporarily, yet also aid intragranular microcracking in adjacent stiff grains and at grain boundaries. Tensile microcrack and microfault average dips from the sample rupture surface increase with rupture normal stress, with conjugate microfault orientation variability at higher normal stresses aiding their connectivity. Results of this investigation demonstrate how the fracture porosity and connectivity around rupture zones increase dramatically at increased rupture normal stress, impacting on hydrodynamic properties of rupture zones.

Photoelastic and numerical investigation of stress distributions around fault models under biaxial compressive loading conditions

Abstract This paper presents the results of a photoelastic and numerical study of stress distributions (contours and trajectories) around fault models of various geometries, submitted to a biaxial compressive load. It aims to describe typical biaxial stress behaviours and emphasize the existing differences with the well-known uniaxial compressive load case. Stress trajectories are sometimes shown by joint sets acting as markers of a paleostress field, and they can be interpreted by particular shallow tension–compression situations. At depth fractures can be reactivated, or can dilate under conditions of triaxial compression, and behaviour is essentially controlled by a high stress ratio (high σ3/σ1 ratio). In spite of the potential importance of such stress states on fracture permeability and fluid flow, and although they are frequently found at depth in a reservoir context, such stress conditions are poorly investigated, particularly in terms of stress perturbations. The presented analogue experiments consisted of compression tests done on polymethylmethacrylate (PMMA) plates; this material has mechanical properties comparable to those of brittle rocks in the upper crust, and presents birefringence. The samples contained open defects acting as faults, and the stress trajectories around these faults were investigated using a photoelastic device. Comparable numerical experiments were realised with a finite-element code (Franc 2D), using frictionless fault models. First, the effect of an increasing biaxial compressive load ratio σ3/σ1 on stress trajectories around an isolated open defect was explored. It was shown that the stress trajectories were drastically modified when σ3/σ1 increased from 0.2 to 0.4, this result being consistent with previous studies. In particular, when σ3/σ1 was superior or equal to 0.4, external isotropic points around where trajectories diverged (called repulsive isotropic points) appeared near the tips, but away from the defects. They tended to move away from the defects towards the main load direction when σ3/σ1 increased. The described isotropic points were points of stress trajectory divergence, i.e. points where stress decreased, implying that zones around them were strongly unfavourable to shear reactivation. Second, stress trajectories around fault models of various geometries (oblique isolated defect, dilational jog, compressive jog, and complex patterns) were studied, the applied biaxial compressive load ratio being 0.7. These biaxial stress trajectories were compared with similar uniaxial stress trajectories in order to explore the existing differences between the two regimes. It enabled new stress trajectory geometries to be described and interpreted. In particular, numerous external repulsive isotropic points were observed, and defect tips were shown to be zones of high convergence of stress trajectories. Furthermore, in contrast to the uniaxial compressive load case, stress trajectories and stress contours were geometrically similar within dilational and compressive jogs under biaxial compressive load. For both jog types, the centre of the overlapping zone, and the areas along the wall of a jog-defining fault and facing the overlapping tip of the other fault, proved to be zones of low mean stress, implying that fluids may migrate towards them from the tips of the faults, in response to mean stress gradients. Furthermore, the centre of the jogs exhibiting a high differential stress was a favourable area in terms of fracture reactivation, which may facilitate fluids transfer and storage. It was also observed that for both the uniaxial and biaxial compressive loads, isotropic zones were localised at the acute angle between branching defects.

Normal load, slip rate and roughness influence on the polymethylmethacrylate dynamics of sliding. 1. Stable sliding to stick-slip transition

We present the results from an extensive study on (PMMA)-PMMA polymethylmethacrylate dry friction. For a wide range of normal pressures, slip rates and grades of roughness of sliding surfaces, we analysed the conditions in which steady and catastrophic sliding appear. For the grades of roughness and slip rates investigated, we observed a steady-state regime at low normal pressures and a stick-slip regime when the normal pressures were high. For intermediate normal pressures, the transition between the two regimes was controlled by the roughness and slip rates. In this last case, slip motion was steady at high slip rates for the range of grades of roughness considered, and at all slip rates for the roughest surfaces. In other conditions, we observed stick-slip. In the case of steady sliding, the dynamic coefficient of friction decreased linearly with the logarithm of increasing sliding velocity. Furthermore, this coefficient of friction and its variations with slip velocity were lower for smooth surfaces. For stick-slip motion, the static coefficient of friction was mostly influenced by normal pressure. For the three highest normal pressures, the static coefficient of friction decreased linearly when normal pressure increased. This coefficient was not influenced by slip rate and showed a slight increase when the roughness of the sliding surfaces increased.

Experimental evidence of contact loss during stick-slip: possible implications for seismic behaviour

Abstract We present results of an experimental study on the stick-slip phenomenon focused on detailed measurements of the relative normal displacement. This was done mainly to determine whether or not the sliding surfaces become separated during the slip phase as suggested in previous works. Experiments were performed on PMMA as it has mechanical properties comparable to those of brittle rocks and has proved to be a good analogue for rocks in rupture mechanics experiments. Results show clearly that normal displacement occurs during and after the slip phase. The characterisation of the sliding surface enables us to compare the maximum relative normal displacement during the slip phase with asperity height. In most cases, the maximum relative normal displacement was found to be higher than the average value of the peak-to-trough relief of the surface, showing that sliding surfaces were at least partially separated. The phenomenon generally consists of a monotonous slip opening phase followed by a monotonous slip closure phase. In some cases, the slip closure phase shows oscillations which have been interpreted as elastic bounces. This last phenomenon was observed irrespective of the experimental conditions with a probability ranging from 0.1 to 0.3 but no clear variations of this probability have been found as a function of normal stress and roughness. These observations may give insights for the explanations of earthquake-related problems such as the heat flow paradox, anomalous P-wave radiation or the inferred low average friction coefficients in subduction zones.

Normal load, slip rate and roughness influence on the PMMA dynamics of sliding 2. Characterisation of the stick-slip phenomenon

We performed an extensive study on PMMA-PMMA dry friction. For a wide range of normal pressures, slip rates and grades of roughness of sliding surfaces we focused on the detailed characterisation of the stick-slip motion. With an original experimental device associated with a high speed data acquisition system, we measured six parameters: the distance and the duration of slip, the maximum velocity during slip motion, the relative displacement and/or deformation during the stick phase and the duration of this phase, and the number of events per millimeter of displacement. We observed that all parameters are strongly influenced by normal pressure and do not vary according to the slip rate apart from the duration of stick which was mostly influenced by slip rate. Furthermore, apart from the duration of slip, all parameters are influenced by roughness.